Average Error: 2.8 → 0.0
Time: 8.0s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r373892 = x;
        double r373893 = y;
        double r373894 = 1.1283791670955126;
        double r373895 = z;
        double r373896 = exp(r373895);
        double r373897 = r373894 * r373896;
        double r373898 = r373892 * r373893;
        double r373899 = r373897 - r373898;
        double r373900 = r373893 / r373899;
        double r373901 = r373892 + r373900;
        return r373901;
}
↓
double f(double x, double y, double z) {
        double r373902 = x;
        double r373903 = 1.0;
        double r373904 = 1.1283791670955126;
        double r373905 = z;
        double r373906 = exp(r373905);
        double r373907 = r373904 * r373906;
        double r373908 = y;
        double r373909 = r373907 / r373908;
        double r373910 = r373909 - r373902;
        double r373911 = r373903 / r373910;
        double r373912 = r373902 + r373911;
        return r373912;
}

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

Original2.8
Target0.1
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.9

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

  5. Applied div-sub2.9

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019291 
(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)))))