Average Error: 0.2 → 0.2
Time: 4.2s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\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[3]{\sqrt[3]{3}}\right) \cdot y
double f(double x, double y) {
        double r891444 = x;
        double r891445 = 16.0;
        double r891446 = 116.0;
        double r891447 = r891445 / r891446;
        double r891448 = r891444 - r891447;
        double r891449 = 3.0;
        double r891450 = r891448 * r891449;
        double r891451 = y;
        double r891452 = r891450 * r891451;
        return r891452;
}
↓
double f(double x, double y) {
        double r891453 = x;
        double r891454 = 16.0;
        double r891455 = 116.0;
        double r891456 = r891454 / r891455;
        double r891457 = r891453 - r891456;
        double r891458 = 3.0;
        double r891459 = cbrt(r891458);
        double r891460 = 2.0;
        double r891461 = pow(r891459, r891460);
        double r891462 = r891459 * r891459;
        double r891463 = cbrt(r891462);
        double r891464 = r891461 * r891463;
        double r891465 = r891457 * r891464;
        double r891466 = cbrt(r891459);
        double r891467 = r891465 * r891466;
        double r891468 = y;
        double r891469 = r891467 * r891468;
        return r891469;
}

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

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

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