Average Error: 0.1 → 0.7
Time: 10.8s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r166422 = x;
        double r166423 = y;
        double r166424 = cos(r166423);
        double r166425 = r166422 * r166424;
        double r166426 = z;
        double r166427 = sin(r166423);
        double r166428 = r166426 * r166427;
        double r166429 = r166425 + r166428;
        return r166429;
}
↓
double f(double x, double y, double z) {
        double r166430 = x;
        double r166431 = y;
        double r166432 = cos(r166431);
        double r166433 = r166430 * r166432;
        double r166434 = z;
        double r166435 = cbrt(r166434);
        double r166436 = r166435 * r166435;
        double r166437 = cbrt(r166436);
        double r166438 = r166437 * r166437;
        double r166439 = cbrt(r166435);
        double r166440 = r166439 * r166439;
        double r166441 = r166438 * r166440;
        double r166442 = sin(r166431);
        double r166443 = r166435 * r166442;
        double r166444 = r166441 * r166443;
        double r166445 = r166433 + r166444;
        return r166445;
}

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

Derivation

  1. Initial program 0.1

    \[x \cdot \cos y + z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.6

    \[\leadsto x \cdot \cos y + \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \sin y\]

  4. Applied associate-*l*0.6

    \[\leadsto x \cdot \cos y + \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.6

    \[\leadsto x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

  7. Applied cbrt-prod0.6

    \[\leadsto x \cdot \cos y + \left(\sqrt[3]{z} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

  8. Applied add-cube-cbrt0.7

    \[\leadsto x \cdot \cos y + \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}} \cdot \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

  9. Applied cbrt-prod0.7

    \[\leadsto x \cdot \cos y + \left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

  10. Applied swap-sqr0.7

    \[\leadsto x \cdot \cos y + \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right)} \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

  11. Final simplification0.7

    \[\leadsto x \cdot \cos y + \left(\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))