Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)
double f(double x) {
        double r93794 = 2.30753;
        double r93795 = x;
        double r93796 = 0.27061;
        double r93797 = r93795 * r93796;
        double r93798 = r93794 + r93797;
        double r93799 = 1.0;
        double r93800 = 0.99229;
        double r93801 = 0.04481;
        double r93802 = r93795 * r93801;
        double r93803 = r93800 + r93802;
        double r93804 = r93795 * r93803;
        double r93805 = r93799 + r93804;
        double r93806 = r93798 / r93805;
        double r93807 = r93806 - r93795;
        return r93807;
}
↓
double f(double x) {
        double r93808 = 2.30753;
        double r93809 = x;
        double r93810 = 0.27061;
        double r93811 = r93809 * r93810;
        double r93812 = r93808 + r93811;
        double r93813 = 1.0;
        double r93814 = 1.0;
        double r93815 = 0.99229;
        double r93816 = 0.04481;
        double r93817 = r93809 * r93816;
        double r93818 = r93815 + r93817;
        double r93819 = r93809 * r93818;
        double r93820 = r93814 + r93819;
        double r93821 = r93813 / r93820;
        double r93822 = -r93809;
        double r93823 = fma(r93812, r93821, r93822);
        return r93823;
}

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. Applied fma-neg0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 +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))