Average Error: 3.1 → 0.2
Time: 14.8s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{\sqrt[3]{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}{y} - x} + x\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{\sqrt[3]{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}{y} - x} + x
double f(double x, double y, double z) {
        double r20892909 = x;
        double r20892910 = y;
        double r20892911 = 1.1283791670955126;
        double r20892912 = z;
        double r20892913 = exp(r20892912);
        double r20892914 = r20892911 * r20892913;
        double r20892915 = r20892909 * r20892910;
        double r20892916 = r20892914 - r20892915;
        double r20892917 = r20892910 / r20892916;
        double r20892918 = r20892909 + r20892917;
        return r20892918;
}
↓
double f(double x, double y, double z) {
        double r20892919 = 1.0;
        double r20892920 = z;
        double r20892921 = exp(r20892920);
        double r20892922 = 1.1283791670955126;
        double r20892923 = r20892921 * r20892922;
        double r20892924 = r20892923 * r20892923;
        double r20892925 = r20892923 * r20892924;
        double r20892926 = cbrt(r20892925);
        double r20892927 = y;
        double r20892928 = r20892926 / r20892927;
        double r20892929 = x;
        double r20892930 = r20892928 - r20892929;
        double r20892931 = r20892919 / r20892930;
        double r20892932 = r20892931 + r20892929;
        return r20892932;
}

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

Original3.1
Target0.0
Herbie0.2
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.1

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num3.1

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub3.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \color{blue}{x}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube0.0

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot \color{blue}{\sqrt[3]{\left(e^{z} \cdot e^{z}\right) \cdot e^{z}}}}{y} - x}\]

  9. Applied add-cbrt-cube0.2

    \[\leadsto x + \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(1.1283791670955126 \cdot 1.1283791670955126\right) \cdot 1.1283791670955126}} \cdot \sqrt[3]{\left(e^{z} \cdot e^{z}\right) \cdot e^{z}}}{y} - x}\]

  10. Applied cbrt-unprod0.2

    \[\leadsto x + \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(\left(1.1283791670955126 \cdot 1.1283791670955126\right) \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot e^{z}\right) \cdot e^{z}\right)}}}{y} - x}\]

  11. Simplified0.2

    \[\leadsto x + \frac{1}{\frac{\sqrt[3]{\color{blue}{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}}{y} - x}\]

  12. Final simplification0.2

    \[\leadsto \frac{1}{\frac{\sqrt[3]{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}{y} - x} + x\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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