Average Error: 0.2 → 0.6
Time: 14.9s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(\left(x - \frac{16}{{\left(\sqrt[3]{116}\right)}^{3}}\right) + \left(\left(-\frac{16}{{\left(\sqrt[3]{116}\right)}^{3}}\right) + \frac{16}{{\left(\sqrt[3]{116}\right)}^{3}}\right)\right) \cdot 3\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(\left(x - \frac{16}{{\left(\sqrt[3]{116}\right)}^{3}}\right) + \left(\left(-\frac{16}{{\left(\sqrt[3]{116}\right)}^{3}}\right) + \frac{16}{{\left(\sqrt[3]{116}\right)}^{3}}\right)\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r499839 = x;
        double r499840 = 16.0;
        double r499841 = 116.0;
        double r499842 = r499840 / r499841;
        double r499843 = r499839 - r499842;
        double r499844 = 3.0;
        double r499845 = r499843 * r499844;
        double r499846 = y;
        double r499847 = r499845 * r499846;
        return r499847;
}
↓
double f(double x, double y) {
        double r499848 = x;
        double r499849 = 16.0;
        double r499850 = 116.0;
        double r499851 = cbrt(r499850);
        double r499852 = 3.0;
        double r499853 = pow(r499851, r499852);
        double r499854 = r499849 / r499853;
        double r499855 = r499848 - r499854;
        double r499856 = -r499854;
        double r499857 = r499856 + r499854;
        double r499858 = r499855 + r499857;
        double r499859 = 3.0;
        double r499860 = r499858 * r499859;
        double r499861 = y;
        double r499862 = r499860 * r499861;
        return r499862;
}

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
Herbie0.6
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

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-cbrt0.6

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

  4. Applied add-cube-cbrt1.5

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

  5. Applied times-frac1.6

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

  6. Applied add-sqr-sqrt33.2

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

  7. Applied prod-diff33.2

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

  8. Simplified0.6

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

  9. Simplified0.6

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

  10. Final simplification0.6

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(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))