Average Error: 0.1 → 0.2
Time: 9.5s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)
double f(double x) {
        double r97892 = 1.0;
        double r97893 = x;
        double r97894 = 0.253;
        double r97895 = 0.12;
        double r97896 = r97893 * r97895;
        double r97897 = r97894 + r97896;
        double r97898 = r97893 * r97897;
        double r97899 = r97892 - r97898;
        return r97899;
}
↓
double f(double x) {
        double r97900 = 1.0;
        double r97901 = 0.12;
        double r97902 = x;
        double r97903 = 2.0;
        double r97904 = pow(r97902, r97903);
        double r97905 = r97901 * r97904;
        double r97906 = 0.253;
        double r97907 = r97906 * r97902;
        double r97908 = r97905 + r97907;
        double r97909 = r97900 - r97908;
        return r97909;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto 1 - x \cdot \color{blue}{\left(\left(\sqrt[3]{0.253 + x \cdot 0.12} \cdot \sqrt[3]{0.253 + x \cdot 0.12}\right) \cdot \sqrt[3]{0.253 + x \cdot 0.12}\right)}\]

  4. Applied associate-*r*0.4

    \[\leadsto 1 - \color{blue}{\left(x \cdot \left(\sqrt[3]{0.253 + x \cdot 0.12} \cdot \sqrt[3]{0.253 + x \cdot 0.12}\right)\right) \cdot \sqrt[3]{0.253 + x \cdot 0.12}}\]

  5. Taylor expanded around 0 0.2

    \[\leadsto 1 - \color{blue}{\left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)}\]

  6. Final simplification0.2

    \[\leadsto 1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))