Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)} - x
double f(double x) {
        double r40131 = 2.30753;
        double r40132 = x;
        double r40133 = 0.27061;
        double r40134 = r40132 * r40133;
        double r40135 = r40131 + r40134;
        double r40136 = 1.0;
        double r40137 = 0.99229;
        double r40138 = 0.04481;
        double r40139 = r40132 * r40138;
        double r40140 = r40137 + r40139;
        double r40141 = r40132 * r40140;
        double r40142 = r40136 + r40141;
        double r40143 = r40135 / r40142;
        double r40144 = r40143 - r40132;
        return r40144;
}
↓
double f(double x) {
        double r40145 = 2.30753;
        double r40146 = x;
        double r40147 = 0.27061;
        double r40148 = r40146 * r40147;
        double r40149 = r40145 + r40148;
        double r40150 = 1.0;
        double r40151 = 0.04481;
        double r40152 = 0.99229;
        double r40153 = fma(r40151, r40146, r40152);
        double r40154 = 1.0;
        double r40155 = fma(r40146, r40153, r40154);
        double r40156 = r40150 / r40155;
        double r40157 = r40149 * r40156;
        double r40158 = r40157 - r40146;
        return r40158;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto \color{blue}{\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

  4. Simplified0.0

    \[\leadsto \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}} - x\]

  5. Final simplification0.0

    \[\leadsto \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)} - x\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))