Average Error: 0.2 → 0.3
Time: 13.8s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(y \cdot \left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(y \cdot \left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}
double f(double x, double y) {
        double r679357 = x;
        double r679358 = 16.0;
        double r679359 = 116.0;
        double r679360 = r679358 / r679359;
        double r679361 = r679357 - r679360;
        double r679362 = 3.0;
        double r679363 = r679361 * r679362;
        double r679364 = y;
        double r679365 = r679363 * r679364;
        return r679365;
}
↓
double f(double x, double y) {
        double r679366 = y;
        double r679367 = x;
        double r679368 = 16.0;
        double r679369 = 116.0;
        double r679370 = r679368 / r679369;
        double r679371 = r679367 - r679370;
        double r679372 = 3.0;
        double r679373 = cbrt(r679372);
        double r679374 = 2.0;
        double r679375 = pow(r679373, r679374);
        double r679376 = r679373 * r679373;
        double r679377 = cbrt(r679376);
        double r679378 = r679375 * r679377;
        double r679379 = r679371 * r679378;
        double r679380 = r679366 * r679379;
        double r679381 = cbrt(r679373);
        double r679382 = r679380 * r679381;
        return r679382;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

    \[\leadsto \left(\left(x - \frac{16}{116}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)}\right) \cdot y\]

  4. Applied associate-*r*0.8

    \[\leadsto \color{blue}{\left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}\right)} \cdot y\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.8

    \[\leadsto \left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}}\right) \cdot y\]

  7. Applied cbrt-prod0.8

    \[\leadsto \left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right)}\right) \cdot y\]

  8. Applied associate-*r*0.7

    \[\leadsto \color{blue}{\left(\left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right)} \cdot y\]

  9. Simplified0.2

    \[\leadsto \left(\color{blue}{\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.2

    \[\leadsto \left(\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{\sqrt[3]{3}}} \cdot \sqrt{\sqrt[3]{\sqrt[3]{3}}}\right)}\right) \cdot y\]

  12. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt[3]{3}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt[3]{3}}}\right)} \cdot y\]

  13. Final simplification0.3

    \[\leadsto \left(y \cdot \left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\]

Reproduce

herbie shell --seed 2019294 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

  (* (* (- x (/ 16 116)) 3) y))