Average Error: 3.0 → 0.1
Time: 14.6s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x} + x\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x} + x
double f(double x, double y, double z) {
        double r328725 = x;
        double r328726 = y;
        double r328727 = 1.1283791670955126;
        double r328728 = z;
        double r328729 = exp(r328728);
        double r328730 = r328727 * r328729;
        double r328731 = r328725 * r328726;
        double r328732 = r328730 - r328731;
        double r328733 = r328726 / r328732;
        double r328734 = r328725 + r328733;
        return r328734;
}
↓
double f(double x, double y, double z) {
        double r328735 = 1.0;
        double r328736 = 1.1283791670955126;
        double r328737 = y;
        double r328738 = r328736 / r328737;
        double r328739 = z;
        double r328740 = exp(r328739);
        double r328741 = r328738 * r328740;
        double r328742 = x;
        double r328743 = r328741 - r328742;
        double r328744 = r328735 / r328743;
        double r328745 = r328744 + r328742;
        return r328745;
}

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

Original3.0
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

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

  3. Applied clear-num3.0

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

  5. Applied add-cube-cbrt3.0

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

  6. Applied associate-/l*3.0

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))