An approximate function calculation apparatus, comprising, when x 0 and x 1 represent predetermined numbers satisfying a relationship expressed as x 0 < x 1 , D = [x 0 , x 1 ] represents a section in which a function f(x) is to be approximated, ε represents a predetermined number that is an error allowed in approximation, k represents a predetermined integer equal to or larger than 0, b represents a number satisfying a relationship expressed as x 0 < b <x 1 , and a function g b (x) represents a Taylor expansion of the function f(x) up to a k-th degree at b: a Taylor expansion unit which obtains the function g b (x) ; a first error upper bound calculating unit which obtains an upper bound of an error of an approximation of the function f(x) by the function g b (x) in a section [x 0 , b] ; an expansion position calculating unit which obtains, using upper bounds of errors each being obtained by performing processing by the Taylor expansion unit and the first error upper bound calculating unit for different b, an expansion position b' that represents a maximum b at which the upper bound of an error of an approximation of the function f(x) by the function g b (x) in the section [x 0 , b] is equal to or smaller than ε; a second error upper bound calculating unit which obtains an upper bound of an error of an approximation of the function f(x) by a function g b' (x) in a section [b', x 2 ], where x 2 represents a number satisfying b' < x 2 ≤ x 1 ; a right end position calculating unit which calculates a right end position x 2 ' that represents a maximum x 2 at which the upper bound of an error of an approximation of the function f(x) by the function g b' in the section [b', x 2 ] is equal to or smaller than ε using the upper bound of error obtained by processing by the second error upper bound calculating unit ; an output unit which outputs information related to a section [x 0 , x 2 '] and the function g b' (x), the information being used for secure computation; and a control unit which repeats processing of the Taylor expansion unit , the error upper bound calculating units , the expansion position calculating unit , the right end position calculating unit , and the output unit with a section [x 2 ', x 1 ] as the section D. a Taylor expansion unit which obtains the function g b (x) ; a first error upper bound calculating unit which obtains an upper bound of an error of an approximation of the function f(x) by the function g b (x) in a section [x 0 , b] ; an expansion position calculating unit which obtains, using upper bounds of errors each being obtained by performing processing by the Taylor expansion unit and the first error upper bound calculating unit for different b, an expansion position b' that represents a maximum b at which the upper bound of an error of an approximation of the function f(x) by the function g b (x) in the section [x 0 , b] is equal to or smaller than ε; a second error upper bound calculating unit which obtains an upper bound of an error of an approximation of the function f(x) by a function g b' (x) in a section [b', x 2 ], where x 2 represents a number satisfying b' < x 2 ≤ x 1 ; a right end position calculating unit which calculates a right end position x 2 ' that represents a maximum x 2 at which the upper bound of an error of an approximation of the function f(x) by the function g b' in the section [b', x 2 ] is equal to or smaller than ε using the upper bound of error obtained by processing by the second error upper bound calculating unit ; an output unit which outputs information related to a section [x 0 , x 2 '] and the function g b' (x), the information being used for secure computation; and a control unit which repeats processing of the Taylor expansion unit , the error upper bound calculating units , the expansion position calculating unit , the right end position calculating unit , and the output unit with a section [x 2 ', x 1 ] as the section D. <EOS>