Average Error: 0.1 → 0.5
Time: 20.8s
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 r796563 = x;
        double r796564 = y;
        double r796565 = cos(r796564);
        double r796566 = r796563 * r796565;
        double r796567 = z;
        double r796568 = sin(r796564);
        double r796569 = r796567 * r796568;
        double r796570 = r796566 - r796569;
        return r796570;
}
↓
double f(double x, double y, double z) {
        double r796571 = x;
        double r796572 = y;
        double r796573 = cos(r796572);
        double r796574 = r796571 * r796573;
        double r796575 = z;
        double r796576 = cbrt(r796575);
        double r796577 = sin(r796572);
        double r796578 = cbrt(r796577);
        double r796579 = r796575 * r796577;
        double r796580 = cbrt(r796579);
        double r796581 = r796578 * r796580;
        double r796582 = r796576 * r796581;
        double r796583 = r796582 * r796580;
        double r796584 = r796574 - r796583;
        return r796584;
}

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))))