Average Error: 0.1 → 0.3
Time: 18.0s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(\sqrt[3]{\cos y \cdot \cos y} \cdot z\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left(\sqrt[3]{\cos y \cdot \cos y} \cdot z\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r10483592 = x;
        double r10483593 = y;
        double r10483594 = sin(r10483593);
        double r10483595 = r10483592 * r10483594;
        double r10483596 = z;
        double r10483597 = cos(r10483593);
        double r10483598 = r10483596 * r10483597;
        double r10483599 = r10483595 + r10483598;
        return r10483599;
}
↓
double f(double x, double y, double z) {
        double r10483600 = y;
        double r10483601 = cos(r10483600);
        double r10483602 = cbrt(r10483601);
        double r10483603 = r10483601 * r10483601;
        double r10483604 = cbrt(r10483603);
        double r10483605 = z;
        double r10483606 = r10483604 * r10483605;
        double r10483607 = r10483602 * r10483606;
        double r10483608 = x;
        double r10483609 = sin(r10483600);
        double r10483610 = r10483608 * r10483609;
        double r10483611 = r10483607 + r10483610;
        return r10483611;
}

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. Using strategy rm

  6. Applied cbrt-unprod0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))