Average Error: 2.8 → 0.0
Time: 10.6s
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 r515883 = x;
        double r515884 = y;
        double r515885 = 1.1283791670955126;
        double r515886 = z;
        double r515887 = exp(r515886);
        double r515888 = r515885 * r515887;
        double r515889 = r515883 * r515884;
        double r515890 = r515888 - r515889;
        double r515891 = r515884 / r515890;
        double r515892 = r515883 + r515891;
        return r515892;
}
↓
double f(double x, double y, double z) {
        double r515893 = x;
        double r515894 = 1.0;
        double r515895 = 1.1283791670955126;
        double r515896 = z;
        double r515897 = exp(r515896);
        double r515898 = r515895 * r515897;
        double r515899 = y;
        double r515900 = r515898 / r515899;
        double r515901 = r515900 - r515893;
        double r515902 = r515894 / r515901;
        double r515903 = r515893 + r515902;
        return r515903;
}

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

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  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 2020047 +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)))))