Average Error: 2.6 → 0.0
Time: 13.4s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}
double f(double x, double y, double z) {
        double r20298641 = x;
        double r20298642 = y;
        double r20298643 = 1.1283791670955126;
        double r20298644 = z;
        double r20298645 = exp(r20298644);
        double r20298646 = r20298643 * r20298645;
        double r20298647 = r20298641 * r20298642;
        double r20298648 = r20298646 - r20298647;
        double r20298649 = r20298642 / r20298648;
        double r20298650 = r20298641 + r20298649;
        return r20298650;
}
↓
double f(double x, double y, double z) {
        double r20298651 = x;
        double r20298652 = 1.0;
        double r20298653 = z;
        double r20298654 = exp(r20298653);
        double r20298655 = 1.1283791670955126;
        double r20298656 = r20298654 * r20298655;
        double r20298657 = y;
        double r20298658 = r20298656 / r20298657;
        double r20298659 = r20298658 - r20298651;
        double r20298660 = r20298652 / r20298659;
        double r20298661 = r20298651 + r20298660;
        return r20298661;
}

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

Original2.6
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.6

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

  3. Applied clear-num2.6

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

  5. Applied div-sub2.6

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))