Average Error: 2.7 → 0.0
Time: 9.3s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{\sqrt[3]{e^{z}} \cdot \sqrt[3]{e^{z}}}{\frac{y}{1.128379167095512558560699289955664426088 \cdot \sqrt[3]{e^{z}}}} - x} + x\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{\sqrt[3]{e^{z}} \cdot \sqrt[3]{e^{z}}}{\frac{y}{1.128379167095512558560699289955664426088 \cdot \sqrt[3]{e^{z}}}} - x} + x
double f(double x, double y, double z) {
        double r348840 = x;
        double r348841 = y;
        double r348842 = 1.1283791670955126;
        double r348843 = z;
        double r348844 = exp(r348843);
        double r348845 = r348842 * r348844;
        double r348846 = r348840 * r348841;
        double r348847 = r348845 - r348846;
        double r348848 = r348841 / r348847;
        double r348849 = r348840 + r348848;
        return r348849;
}
↓
double f(double x, double y, double z) {
        double r348850 = 1.0;
        double r348851 = z;
        double r348852 = exp(r348851);
        double r348853 = cbrt(r348852);
        double r348854 = r348853 * r348853;
        double r348855 = y;
        double r348856 = 1.1283791670955126;
        double r348857 = r348856 * r348853;
        double r348858 = r348855 / r348857;
        double r348859 = r348854 / r348858;
        double r348860 = x;
        double r348861 = r348859 - r348860;
        double r348862 = r348850 / r348861;
        double r348863 = r348862 + r348860;
        return r348863;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

    \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.7

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]

  4. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} - 1 \cdot x}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.0

    \[\leadsto x + \frac{1}{\frac{\color{blue}{\left(\sqrt[3]{e^{z}} \cdot \sqrt[3]{e^{z}}\right) \cdot \sqrt[3]{e^{z}}}}{\frac{y}{1.128379167095512558560699289955664426088}} - 1 \cdot x}\]

  7. Applied associate-/l*0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\sqrt[3]{e^{z}} \cdot \sqrt[3]{e^{z}}}{\frac{\frac{y}{1.128379167095512558560699289955664426088}}{\sqrt[3]{e^{z}}}}} - 1 \cdot x}\]

  8. Simplified0.0

    \[\leadsto x + \frac{1}{\frac{\sqrt[3]{e^{z}} \cdot \sqrt[3]{e^{z}}}{\color{blue}{\frac{y}{1.128379167095512558560699289955664426088 \cdot \sqrt[3]{e^{z}}}}} - 1 \cdot x}\]

  9. Final simplification0.0

    \[\leadsto \frac{1}{\frac{\sqrt[3]{e^{z}} \cdot \sqrt[3]{e^{z}}}{\frac{y}{1.128379167095512558560699289955664426088 \cdot \sqrt[3]{e^{z}}}} - x} + x\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))