Average Error: 0.1 → 0.5
Time: 21.0s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r180641 = x;
        double r180642 = y;
        double r180643 = cos(r180642);
        double r180644 = r180641 * r180643;
        double r180645 = z;
        double r180646 = sin(r180642);
        double r180647 = r180645 * r180646;
        double r180648 = r180644 - r180647;
        return r180648;
}
↓
double f(double x, double y, double z) {
        double r180649 = x;
        double r180650 = y;
        double r180651 = cos(r180650);
        double r180652 = r180649 * r180651;
        double r180653 = z;
        double r180654 = cbrt(r180653);
        double r180655 = sin(r180650);
        double r180656 = cbrt(r180655);
        double r180657 = r180653 * r180655;
        double r180658 = cbrt(r180657);
        double r180659 = r180656 * r180658;
        double r180660 = r180654 * r180659;
        double r180661 = r180660 * r180658;
        double r180662 = r180652 - r180661;
        return r180662;
}

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

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

  5. Applied cbrt-prod0.5

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))