Average Error: 0.1 → 0.6
Time: 15.6s
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 r169216 = x;
        double r169217 = y;
        double r169218 = cos(r169217);
        double r169219 = r169216 * r169218;
        double r169220 = z;
        double r169221 = sin(r169217);
        double r169222 = r169220 * r169221;
        double r169223 = r169219 - r169222;
        return r169223;
}
↓
double f(double x, double y, double z) {
        double r169224 = x;
        double r169225 = y;
        double r169226 = cos(r169225);
        double r169227 = r169224 * r169226;
        double r169228 = sin(r169225);
        double r169229 = cbrt(r169228);
        double r169230 = z;
        double r169231 = r169229 * r169230;
        double r169232 = r169231 * r169229;
        double r169233 = r169232 * r169229;
        double r169234 = r169227 - r169233;
        return r169234;
}

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))))