Average Error: 2.7 → 0.0
Time: 7.1s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r285893 = x;
        double r285894 = y;
        double r285895 = 1.1283791670955126;
        double r285896 = z;
        double r285897 = exp(r285896);
        double r285898 = r285895 * r285897;
        double r285899 = r285893 * r285894;
        double r285900 = r285898 - r285899;
        double r285901 = r285894 / r285900;
        double r285902 = r285893 + r285901;
        return r285902;
}
↓
double f(double x, double y, double z) {
        double r285903 = x;
        double r285904 = 1.0;
        double r285905 = 1.1283791670955126;
        double r285906 = z;
        double r285907 = exp(r285906);
        double r285908 = r285905 * r285907;
        double r285909 = y;
        double r285910 = r285908 / r285909;
        double r285911 = r285910 - r285903;
        double r285912 = r285904 / r285911;
        double r285913 = r285903 + r285912;
        return r285913;
}

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

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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)))))