Average Error: 0.2 → 0.2
Time: 4.5s
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 r766193 = x;
        double r766194 = 16.0;
        double r766195 = 116.0;
        double r766196 = r766194 / r766195;
        double r766197 = r766193 - r766196;
        double r766198 = 3.0;
        double r766199 = r766197 * r766198;
        double r766200 = y;
        double r766201 = r766199 * r766200;
        return r766201;
}
↓
double f(double x, double y) {
        double r766202 = x;
        double r766203 = 16.0;
        double r766204 = 116.0;
        double r766205 = r766203 / r766204;
        double r766206 = r766202 - r766205;
        double r766207 = 3.0;
        double r766208 = cbrt(r766207);
        double r766209 = 2.0;
        double r766210 = pow(r766208, r766209);
        double r766211 = r766208 * r766208;
        double r766212 = cbrt(r766211);
        double r766213 = r766210 * r766212;
        double r766214 = r766206 * r766213;
        double r766215 = cbrt(r766208);
        double r766216 = r766214 * r766215;
        double r766217 = y;
        double r766218 = r766216 * r766217;
        return r766218;
}

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 +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))