Average Error: 2.9 → 0.0
Time: 3.0s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{\sqrt{1}}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{\sqrt{1}}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r396046 = x;
        double r396047 = y;
        double r396048 = 1.1283791670955126;
        double r396049 = z;
        double r396050 = exp(r396049);
        double r396051 = r396048 * r396050;
        double r396052 = r396046 * r396047;
        double r396053 = r396051 - r396052;
        double r396054 = r396047 / r396053;
        double r396055 = r396046 + r396054;
        return r396055;
}
↓
double f(double x, double y, double z) {
        double r396056 = x;
        double r396057 = 1.0;
        double r396058 = sqrt(r396057);
        double r396059 = 1.1283791670955126;
        double r396060 = z;
        double r396061 = exp(r396060);
        double r396062 = r396059 * r396061;
        double r396063 = y;
        double r396064 = r396062 / r396063;
        double r396065 = r396064 - r396056;
        double r396066 = r396058 / r396065;
        double r396067 = r396056 + r396066;
        return r396067;
}

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

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. Using strategy rm

  5. Applied add-sqr-sqrt2.9

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

  6. Applied associate-/l*2.9

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

  7. Simplified0.1

    \[\leadsto x + \frac{\sqrt{1}}{\color{blue}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}}\]
  8. Using strategy rm

  9. Applied associate-*r/0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 
(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)))))