Average Error: 3.0 → 0.0
Time: 3.2s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}
double f(double x, double y, double z) {
        double r518600 = x;
        double r518601 = y;
        double r518602 = 1.1283791670955126;
        double r518603 = z;
        double r518604 = exp(r518603);
        double r518605 = r518602 * r518604;
        double r518606 = r518600 * r518601;
        double r518607 = r518605 - r518606;
        double r518608 = r518601 / r518607;
        double r518609 = r518600 + r518608;
        return r518609;
}
↓
double f(double x, double y, double z) {
        double r518610 = x;
        double r518611 = 1.0;
        double r518612 = 1.1283791670955126;
        double r518613 = z;
        double r518614 = exp(r518613);
        double r518615 = y;
        double r518616 = r518614 / r518615;
        double r518617 = r518612 * r518616;
        double r518618 = r518610 / r518611;
        double r518619 = r518617 - r518618;
        double r518620 = r518611 / r518619;
        double r518621 = r518610 + r518620;
        return r518621;
}

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

Original3.0
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

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

  3. Applied clear-num3.0

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

  5. Applied div-sub3.0

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

  6. Simplified3.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(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)))))