Average Error: 0.0 → 0.1
Time: 8.8s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x
double f(double x) {
        double r70068 = 2.30753;
        double r70069 = x;
        double r70070 = 0.27061;
        double r70071 = r70069 * r70070;
        double r70072 = r70068 + r70071;
        double r70073 = 1.0;
        double r70074 = 0.99229;
        double r70075 = 0.04481;
        double r70076 = r70069 * r70075;
        double r70077 = r70074 + r70076;
        double r70078 = r70069 * r70077;
        double r70079 = r70073 + r70078;
        double r70080 = r70072 / r70079;
        double r70081 = r70080 - r70069;
        return r70081;
}
↓
double f(double x) {
        double r70082 = 2.30753;
        double r70083 = x;
        double r70084 = 0.27061;
        double r70085 = r70083 * r70084;
        double r70086 = r70082 + r70085;
        double r70087 = 1.0;
        double r70088 = 0.99229;
        double r70089 = 0.04481;
        double r70090 = r70083 * r70089;
        double r70091 = r70088 + r70090;
        double r70092 = r70083 * r70091;
        double r70093 = r70087 + r70092;
        double r70094 = sqrt(r70093);
        double r70095 = r70086 / r70094;
        double r70096 = r70095 / r70094;
        double r70097 = r70096 - r70083;
        return r70097;
}

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 add-sqr-sqrt0.1

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

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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))