Average Error: 2.6 → 0.0
Time: 9.9s
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 r18116618 = x;
        double r18116619 = y;
        double r18116620 = 1.1283791670955126;
        double r18116621 = z;
        double r18116622 = exp(r18116621);
        double r18116623 = r18116620 * r18116622;
        double r18116624 = r18116618 * r18116619;
        double r18116625 = r18116623 - r18116624;
        double r18116626 = r18116619 / r18116625;
        double r18116627 = r18116618 + r18116626;
        return r18116627;
}
↓
double f(double x, double y, double z) {
        double r18116628 = x;
        double r18116629 = 1.0;
        double r18116630 = z;
        double r18116631 = exp(r18116630);
        double r18116632 = 1.1283791670955126;
        double r18116633 = r18116631 * r18116632;
        double r18116634 = y;
        double r18116635 = r18116633 / r18116634;
        double r18116636 = r18116635 - r18116628;
        double r18116637 = r18116629 / r18116636;
        double r18116638 = r18116628 + r18116637;
        return r18116638;
}

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

Original2.6
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.6

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

  3. Applied clear-num2.6

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

  5. Applied div-sub2.6

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(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)))))