Average Error: 2.9 → 0.0
Time: 14.8s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}
double f(double x, double y, double z) {
        double r21469576 = x;
        double r21469577 = y;
        double r21469578 = 1.1283791670955126;
        double r21469579 = z;
        double r21469580 = exp(r21469579);
        double r21469581 = r21469578 * r21469580;
        double r21469582 = r21469576 * r21469577;
        double r21469583 = r21469581 - r21469582;
        double r21469584 = r21469577 / r21469583;
        double r21469585 = r21469576 + r21469584;
        return r21469585;
}
↓
double f(double x, double y, double z) {
        double r21469586 = x;
        double r21469587 = 1.0;
        double r21469588 = z;
        double r21469589 = exp(r21469588);
        double r21469590 = 1.1283791670955126;
        double r21469591 = r21469589 * r21469590;
        double r21469592 = y;
        double r21469593 = r21469591 / r21469592;
        double r21469594 = r21469593 - r21469586;
        double r21469595 = r21469587 / r21469594;
        double r21469596 = r21469586 + r21469595;
        return r21469596;
}

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
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub2.9

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \color{blue}{x}}\]

  7. Final simplification0.0

    \[\leadsto x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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