Average Error: 2.9 → 0.1
Time: 3.0s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}
double f(double x, double y, double z) {
        double r367798 = x;
        double r367799 = y;
        double r367800 = 1.1283791670955126;
        double r367801 = z;
        double r367802 = exp(r367801);
        double r367803 = r367800 * r367802;
        double r367804 = r367798 * r367799;
        double r367805 = r367803 - r367804;
        double r367806 = r367799 / r367805;
        double r367807 = r367798 + r367806;
        return r367807;
}
↓
double f(double x, double y, double z) {
        double r367808 = x;
        double r367809 = 1.0;
        double r367810 = 1.1283791670955126;
        double r367811 = z;
        double r367812 = exp(r367811);
        double r367813 = y;
        double r367814 = r367812 / r367813;
        double r367815 = r367810 * r367814;
        double r367816 = r367808 / r367809;
        double r367817 = r367815 - r367816;
        double r367818 = r367809 / r367817;
        double r367819 = r367808 + r367818;
        return r367819;
}

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

Original2.9
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub2.9

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.12837916709551256 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified2.9

    \[\leadsto x + \frac{1}{\color{blue}{1.12837916709551256 \cdot \frac{e^{z}}{y}} - \frac{x \cdot y}{y}}\]

  7. Simplified0.1

    \[\leadsto x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \color{blue}{\frac{x}{1}}}\]

  8. Final simplification0.1

    \[\leadsto x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

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

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