Average Error: 2.7 → 0.0
Time: 14.0s
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 r21243594 = x;
        double r21243595 = y;
        double r21243596 = 1.1283791670955126;
        double r21243597 = z;
        double r21243598 = exp(r21243597);
        double r21243599 = r21243596 * r21243598;
        double r21243600 = r21243594 * r21243595;
        double r21243601 = r21243599 - r21243600;
        double r21243602 = r21243595 / r21243601;
        double r21243603 = r21243594 + r21243602;
        return r21243603;
}
↓
double f(double x, double y, double z) {
        double r21243604 = x;
        double r21243605 = 1.0;
        double r21243606 = z;
        double r21243607 = exp(r21243606);
        double r21243608 = 1.1283791670955126;
        double r21243609 = y;
        double r21243610 = r21243608 / r21243609;
        double r21243611 = r21243607 * r21243610;
        double r21243612 = r21243611 - r21243604;
        double r21243613 = r21243605 / r21243612;
        double r21243614 = r21243604 + r21243613;
        return r21243614;
}

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

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  5. Applied clear-num2.7

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

  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 2019171 
(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)))))