Average Error: 2.8 → 0.0
Time: 11.8s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{\frac{y}{e^{z}}} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{\frac{y}{e^{z}}} - x}
double f(double x, double y, double z) {
        double r329554 = x;
        double r329555 = y;
        double r329556 = 1.1283791670955126;
        double r329557 = z;
        double r329558 = exp(r329557);
        double r329559 = r329556 * r329558;
        double r329560 = r329554 * r329555;
        double r329561 = r329559 - r329560;
        double r329562 = r329555 / r329561;
        double r329563 = r329554 + r329562;
        return r329563;
}
↓
double f(double x, double y, double z) {
        double r329564 = x;
        double r329565 = 1.0;
        double r329566 = 1.1283791670955126;
        double r329567 = y;
        double r329568 = z;
        double r329569 = exp(r329568);
        double r329570 = r329567 / r329569;
        double r329571 = r329566 / r329570;
        double r329572 = r329571 - r329564;
        double r329573 = r329565 / r329572;
        double r329574 = r329564 + r329573;
        return r329574;
}

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

Original2.8
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

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

  2. Simplified2.8

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

  4. Applied clear-num2.8

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(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)))))