Average Error: 0.1 → 0.6
Time: 23.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r9734647 = x;
        double r9734648 = y;
        double r9734649 = cos(r9734648);
        double r9734650 = r9734647 * r9734649;
        double r9734651 = z;
        double r9734652 = sin(r9734648);
        double r9734653 = r9734651 * r9734652;
        double r9734654 = r9734650 - r9734653;
        return r9734654;
}
↓
double f(double x, double y, double z) {
        double r9734655 = x;
        double r9734656 = y;
        double r9734657 = cos(r9734656);
        double r9734658 = r9734655 * r9734657;
        double r9734659 = sin(r9734656);
        double r9734660 = z;
        double r9734661 = r9734659 * r9734660;
        double r9734662 = cbrt(r9734661);
        double r9734663 = cbrt(r9734659);
        double r9734664 = r9734663 * r9734663;
        double r9734665 = cbrt(r9734660);
        double r9734666 = r9734665 * r9734665;
        double r9734667 = r9734664 * r9734666;
        double r9734668 = r9734662 * r9734667;
        double r9734669 = r9734658 - r9734668;
        return r9734669;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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

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

  6. Applied cbrt-prod0.6

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

  7. Applied swap-sqr0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))