Average Error: 2.7 → 0.0
Time: 6.1s
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 r405726 = x;
        double r405727 = y;
        double r405728 = 1.1283791670955126;
        double r405729 = z;
        double r405730 = exp(r405729);
        double r405731 = r405728 * r405730;
        double r405732 = r405726 * r405727;
        double r405733 = r405731 - r405732;
        double r405734 = r405727 / r405733;
        double r405735 = r405726 + r405734;
        return r405735;
}
↓
double f(double x, double y, double z) {
        double r405736 = x;
        double r405737 = 1.0;
        double r405738 = 1.1283791670955126;
        double r405739 = z;
        double r405740 = exp(r405739);
        double r405741 = r405738 * r405740;
        double r405742 = y;
        double r405743 = r405741 / r405742;
        double r405744 = r405743 - r405736;
        double r405745 = r405737 / r405744;
        double r405746 = r405736 + r405745;
        return r405746;
}

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 +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)))))