Average Error: 0.1 → 0.4
Time: 20.6s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\left(\sqrt[3]{\cos y} \cdot z\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\left(\sqrt[3]{\cos y} \cdot z\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r120608 = x;
        double r120609 = y;
        double r120610 = sin(r120609);
        double r120611 = r120608 * r120610;
        double r120612 = z;
        double r120613 = cos(r120609);
        double r120614 = r120612 * r120613;
        double r120615 = r120611 + r120614;
        return r120615;
}
↓
double f(double x, double y, double z) {
        double r120616 = x;
        double r120617 = y;
        double r120618 = sin(r120617);
        double r120619 = r120616 * r120618;
        double r120620 = cos(r120617);
        double r120621 = cbrt(r120620);
        double r120622 = z;
        double r120623 = r120621 * r120622;
        double r120624 = r120623 * r120621;
        double r120625 = r120624 * r120621;
        double r120626 = r120619 + r120625;
        return r120626;
}

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

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))