Average Error: 0.1 → 0.6
Time: 17.0s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r190116 = x;
        double r190117 = y;
        double r190118 = cos(r190117);
        double r190119 = r190116 * r190118;
        double r190120 = z;
        double r190121 = sin(r190117);
        double r190122 = r190120 * r190121;
        double r190123 = r190119 + r190122;
        return r190123;
}
↓
double f(double x, double y, double z) {
        double r190124 = x;
        double r190125 = y;
        double r190126 = cos(r190125);
        double r190127 = r190124 * r190126;
        double r190128 = z;
        double r190129 = sin(r190125);
        double r190130 = cbrt(r190129);
        double r190131 = r190130 * r190130;
        double r190132 = r190128 * r190131;
        double r190133 = r190132 * r190130;
        double r190134 = r190127 + r190133;
        return r190134;
}

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

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

  6. Final simplification0.6

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

Reproduce

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