Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{1}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}} - x
double f(double x) {
        double r61695 = 2.30753;
        double r61696 = x;
        double r61697 = 0.27061;
        double r61698 = r61696 * r61697;
        double r61699 = r61695 + r61698;
        double r61700 = 1.0;
        double r61701 = 0.99229;
        double r61702 = 0.04481;
        double r61703 = r61696 * r61702;
        double r61704 = r61701 + r61703;
        double r61705 = r61696 * r61704;
        double r61706 = r61700 + r61705;
        double r61707 = r61699 / r61706;
        double r61708 = r61707 - r61696;
        return r61708;
}
↓
double f(double x) {
        double r61709 = 1.0;
        double r61710 = x;
        double r61711 = 0.04481;
        double r61712 = 0.99229;
        double r61713 = fma(r61711, r61710, r61712);
        double r61714 = 1.0;
        double r61715 = fma(r61710, r61713, r61714);
        double r61716 = 0.27061;
        double r61717 = 2.30753;
        double r61718 = fma(r61716, r61710, r61717);
        double r61719 = r61715 / r61718;
        double r61720 = r61709 / r61719;
        double r61721 = r61720 - r61710;
        return r61721;
}

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 clear-num0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +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))