Average Error: 2.8 → 0.0
Time: 11.1s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r379604 = x;
        double r379605 = y;
        double r379606 = 1.1283791670955126;
        double r379607 = z;
        double r379608 = exp(r379607);
        double r379609 = r379606 * r379608;
        double r379610 = r379604 * r379605;
        double r379611 = r379609 - r379610;
        double r379612 = r379605 / r379611;
        double r379613 = r379604 + r379612;
        return r379613;
}
↓
double f(double x, double y, double z) {
        double r379614 = x;
        double r379615 = 1.0;
        double r379616 = 1.1283791670955126;
        double r379617 = z;
        double r379618 = exp(r379617);
        double r379619 = r379616 * r379618;
        double r379620 = y;
        double r379621 = r379619 / r379620;
        double r379622 = r379621 - r379614;
        double r379623 = r379615 / r379622;
        double r379624 = r379614 + r379623;
        return r379624;
}

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. Using strategy rm

  3. Applied clear-num2.8

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

  4. Simplified0.1

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))))