Average Error: 0.1 → 0.6
Time: 5.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r164462 = x;
        double r164463 = y;
        double r164464 = cos(r164463);
        double r164465 = r164462 * r164464;
        double r164466 = z;
        double r164467 = sin(r164463);
        double r164468 = r164466 * r164467;
        double r164469 = r164465 + r164468;
        return r164469;
}
↓
double f(double x, double y, double z) {
        double r164470 = x;
        double r164471 = y;
        double r164472 = cos(r164471);
        double r164473 = r164470 * r164472;
        double r164474 = z;
        double r164475 = cbrt(r164474);
        double r164476 = r164475 * r164475;
        double r164477 = sin(r164471);
        double r164478 = r164475 * r164477;
        double r164479 = r164476 * r164478;
        double r164480 = r164473 + r164479;
        return r164480;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019356 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))