Average Error: 0.1 → 0.6
Time: 16.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\left(\sqrt[3]{\sin y} \cdot z\right) \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{\sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\left(\sqrt[3]{\sin y} \cdot z\right) \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r161758 = x;
        double r161759 = y;
        double r161760 = cos(r161759);
        double r161761 = r161758 * r161760;
        double r161762 = z;
        double r161763 = sin(r161759);
        double r161764 = r161762 * r161763;
        double r161765 = r161761 - r161764;
        return r161765;
}
↓
double f(double x, double y, double z) {
        double r161766 = x;
        double r161767 = y;
        double r161768 = cos(r161767);
        double r161769 = r161766 * r161768;
        double r161770 = sin(r161767);
        double r161771 = cbrt(r161770);
        double r161772 = z;
        double r161773 = r161771 * r161772;
        double r161774 = r161773 * r161771;
        double r161775 = r161774 * r161771;
        double r161776 = r161769 - r161775;
        return r161776;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.1

    \[x \cdot \cos y - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.6

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

  4. Applied associate-*r*0.6

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

  5. Simplified0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))