Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
\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}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
double f(double x) {
        double r55997 = 2.30753;
        double r55998 = x;
        double r55999 = 0.27061;
        double r56000 = r55998 * r55999;
        double r56001 = r55997 + r56000;
        double r56002 = 1.0;
        double r56003 = 0.99229;
        double r56004 = 0.04481;
        double r56005 = r55998 * r56004;
        double r56006 = r56003 + r56005;
        double r56007 = r55998 * r56006;
        double r56008 = r56002 + r56007;
        double r56009 = r56001 / r56008;
        double r56010 = r56009 - r55998;
        return r56010;
}
↓
double f(double x) {
        double r56011 = 2.30753;
        double r56012 = x;
        double r56013 = 0.27061;
        double r56014 = r56012 * r56013;
        double r56015 = r56011 + r56014;
        double r56016 = 1.0;
        double r56017 = 1.0;
        double r56018 = 0.99229;
        double r56019 = 0.04481;
        double r56020 = r56012 * r56019;
        double r56021 = r56018 + r56020;
        double r56022 = r56012 * r56021;
        double r56023 = r56017 + r56022;
        double r56024 = r56016 / r56023;
        double r56025 = r56015 * r56024;
        double r56026 = r56025 - r56012;
        return r56026;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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))