Average Error: 0.1 → 0.6
Time: 18.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r168454 = x;
        double r168455 = y;
        double r168456 = cos(r168455);
        double r168457 = r168454 * r168456;
        double r168458 = z;
        double r168459 = sin(r168455);
        double r168460 = r168458 * r168459;
        double r168461 = r168457 + r168460;
        return r168461;
}
↓
double f(double x, double y, double z) {
        double r168462 = x;
        double r168463 = y;
        double r168464 = cos(r168463);
        double r168465 = r168462 * r168464;
        double r168466 = z;
        double r168467 = cbrt(r168466);
        double r168468 = r168467 * r168467;
        double r168469 = sin(r168463);
        double r168470 = r168469 * r168467;
        double r168471 = r168468 * r168470;
        double r168472 = r168465 + r168471;
        return r168472;
}

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

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))