Average Error: 2.5 → 0.1
Time: 2.3s
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 r436902 = x;
        double r436903 = y;
        double r436904 = 1.1283791670955126;
        double r436905 = z;
        double r436906 = exp(r436905);
        double r436907 = r436904 * r436906;
        double r436908 = r436902 * r436903;
        double r436909 = r436907 - r436908;
        double r436910 = r436903 / r436909;
        double r436911 = r436902 + r436910;
        return r436911;
}
↓
double f(double x, double y, double z) {
        double r436912 = x;
        double r436913 = 1.0;
        double r436914 = 1.1283791670955126;
        double r436915 = z;
        double r436916 = exp(r436915);
        double r436917 = y;
        double r436918 = r436916 / r436917;
        double r436919 = r436914 * r436918;
        double r436920 = r436919 - r436912;
        double r436921 = r436913 / r436920;
        double r436922 = r436912 + r436921;
        return r436922;
}

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

Original2.5
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.5

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

  3. Applied clear-num2.6

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

  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 2020060 +o rules:numerics
(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)))))