Average Error: 2.6 → 0.2
Time: 19.6s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\left(1.128379167095512558560699289955664426088 \cdot \left(\sqrt[3]{\frac{e^{z}}{y}} \cdot \sqrt[3]{\frac{e^{z}}{y}}\right)\right) \cdot \sqrt[3]{\frac{e^{z}}{y}} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\left(1.128379167095512558560699289955664426088 \cdot \left(\sqrt[3]{\frac{e^{z}}{y}} \cdot \sqrt[3]{\frac{e^{z}}{y}}\right)\right) \cdot \sqrt[3]{\frac{e^{z}}{y}} - x}
double f(double x, double y, double z) {
        double r341346 = x;
        double r341347 = y;
        double r341348 = 1.1283791670955126;
        double r341349 = z;
        double r341350 = exp(r341349);
        double r341351 = r341348 * r341350;
        double r341352 = r341346 * r341347;
        double r341353 = r341351 - r341352;
        double r341354 = r341347 / r341353;
        double r341355 = r341346 + r341354;
        return r341355;
}
↓
double f(double x, double y, double z) {
        double r341356 = x;
        double r341357 = 1.0;
        double r341358 = 1.1283791670955126;
        double r341359 = z;
        double r341360 = exp(r341359);
        double r341361 = y;
        double r341362 = r341360 / r341361;
        double r341363 = cbrt(r341362);
        double r341364 = r341363 * r341363;
        double r341365 = r341358 * r341364;
        double r341366 = r341365 * r341363;
        double r341367 = r341366 - r341356;
        double r341368 = r341357 / r341367;
        double r341369 = r341356 + r341368;
        return r341369;
}

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
Target0.1
Herbie0.2
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

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. Simplified0.1

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

  6. Applied add-cube-cbrt0.2

    \[\leadsto x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{e^{z}}{y}} \cdot \sqrt[3]{\frac{e^{z}}{y}}\right) \cdot \sqrt[3]{\frac{e^{z}}{y}}\right)} - x}\]

  7. Applied associate-*r*0.2

    \[\leadsto x + \frac{1}{\color{blue}{\left(1.128379167095512558560699289955664426088 \cdot \left(\sqrt[3]{\frac{e^{z}}{y}} \cdot \sqrt[3]{\frac{e^{z}}{y}}\right)\right) \cdot \sqrt[3]{\frac{e^{z}}{y}}} - x}\]

  8. Final simplification0.2

    \[\leadsto x + \frac{1}{\left(1.128379167095512558560699289955664426088 \cdot \left(\sqrt[3]{\frac{e^{z}}{y}} \cdot \sqrt[3]{\frac{e^{z}}{y}}\right)\right) \cdot \sqrt[3]{\frac{e^{z}}{y}} - x}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))