Average Error: 2.9 → 0.1
Time: 2.8s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r440890 = x;
        double r440891 = y;
        double r440892 = 1.1283791670955126;
        double r440893 = z;
        double r440894 = exp(r440893);
        double r440895 = r440892 * r440894;
        double r440896 = r440890 * r440891;
        double r440897 = r440895 - r440896;
        double r440898 = r440891 / r440897;
        double r440899 = r440890 + r440898;
        return r440899;
}
↓
double f(double x, double y, double z) {
        double r440900 = x;
        double r440901 = 1.0;
        double r440902 = 1.1283791670955126;
        double r440903 = z;
        double r440904 = exp(r440903);
        double r440905 = y;
        double r440906 = r440904 / r440905;
        double r440907 = r440902 * r440906;
        double r440908 = r440907 - r440900;
        double r440909 = r440901 / r440908;
        double r440910 = r440900 + r440909;
        return r440910;
}

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. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 
(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)))))