Average Error: 2.7 → 0.1
Time: 3.3s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - \frac{x}{1}}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - \frac{x}{1}}
double f(double x, double y, double z) {
        double r460331 = x;
        double r460332 = y;
        double r460333 = 1.1283791670955126;
        double r460334 = z;
        double r460335 = exp(r460334);
        double r460336 = r460333 * r460335;
        double r460337 = r460331 * r460332;
        double r460338 = r460336 - r460337;
        double r460339 = r460332 / r460338;
        double r460340 = r460331 + r460339;
        return r460340;
}
↓
double f(double x, double y, double z) {
        double r460341 = x;
        double r460342 = 1.0;
        double r460343 = 1.1283791670955126;
        double r460344 = z;
        double r460345 = exp(r460344);
        double r460346 = y;
        double r460347 = r460345 / r460346;
        double r460348 = r460343 * r460347;
        double r460349 = r460341 / r460342;
        double r460350 = r460348 - r460349;
        double r460351 = r460342 / r460350;
        double r460352 = r460341 + r460351;
        return r460352;
}

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

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 div-sub2.7

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

  6. Simplified2.8

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(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)))))