Average Error: 2.6 → 0.0
Time: 15.7s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}
double f(double x, double y, double z) {
        double r19170616 = x;
        double r19170617 = y;
        double r19170618 = 1.1283791670955126;
        double r19170619 = z;
        double r19170620 = exp(r19170619);
        double r19170621 = r19170618 * r19170620;
        double r19170622 = r19170616 * r19170617;
        double r19170623 = r19170621 - r19170622;
        double r19170624 = r19170617 / r19170623;
        double r19170625 = r19170616 + r19170624;
        return r19170625;
}
↓
double f(double x, double y, double z) {
        double r19170626 = x;
        double r19170627 = 1.0;
        double r19170628 = z;
        double r19170629 = exp(r19170628);
        double r19170630 = 1.1283791670955126;
        double r19170631 = y;
        double r19170632 = r19170630 / r19170631;
        double r19170633 = r19170629 * r19170632;
        double r19170634 = r19170633 - r19170626;
        double r19170635 = r19170627 / r19170634;
        double r19170636 = r19170626 + r19170635;
        return r19170636;
}

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 clear-num2.6

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(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)))))