Average Error: 2.9 → 0.0
Time: 8.7s
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 r404604 = x;
        double r404605 = y;
        double r404606 = 1.1283791670955126;
        double r404607 = z;
        double r404608 = exp(r404607);
        double r404609 = r404606 * r404608;
        double r404610 = r404604 * r404605;
        double r404611 = r404609 - r404610;
        double r404612 = r404605 / r404611;
        double r404613 = r404604 + r404612;
        return r404613;
}
↓
double f(double x, double y, double z) {
        double r404614 = x;
        double r404615 = 1.0;
        double r404616 = z;
        double r404617 = exp(r404616);
        double r404618 = 1.1283791670955126;
        double r404619 = r404617 * r404618;
        double r404620 = y;
        double r404621 = r404619 / r404620;
        double r404622 = r404621 - r404614;
        double r404623 = r404615 / r404622;
        double r404624 = r404614 + r404623;
        return r404624;
}

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

Derivation

  1. Initial program 2.9

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

  3. Applied clear-num2.9

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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)))))