Average Error: 0.1 → 0.4
Time: 20.2s
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 r122639 = x;
        double r122640 = y;
        double r122641 = sin(r122640);
        double r122642 = r122639 * r122641;
        double r122643 = z;
        double r122644 = cos(r122640);
        double r122645 = r122643 * r122644;
        double r122646 = r122642 + r122645;
        return r122646;
}
↓
double f(double x, double y, double z) {
        double r122647 = x;
        double r122648 = y;
        double r122649 = sin(r122648);
        double r122650 = r122647 * r122649;
        double r122651 = cos(r122648);
        double r122652 = cbrt(r122651);
        double r122653 = z;
        double r122654 = r122652 * r122653;
        double r122655 = r122654 * r122652;
        double r122656 = r122655 * r122652;
        double r122657 = r122650 + r122656;
        return r122657;
}

Error

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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

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

  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 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))