Average Error: 0.1 → 0.4
Time: 19.0s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right) \cdot \left(\sqrt[3]{\cos y} \cdot x\right)\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right) \cdot \left(\sqrt[3]{\cos y} \cdot x\right)\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r768594 = x;
        double r768595 = y;
        double r768596 = cos(r768595);
        double r768597 = r768594 * r768596;
        double r768598 = z;
        double r768599 = sin(r768595);
        double r768600 = r768598 * r768599;
        double r768601 = r768597 - r768600;
        return r768601;
}
↓
double f(double x, double y, double z) {
        double r768602 = y;
        double r768603 = cos(r768602);
        double r768604 = cbrt(r768603);
        double r768605 = cbrt(r768604);
        double r768606 = r768605 * r768605;
        double r768607 = r768605 * r768606;
        double r768608 = x;
        double r768609 = r768604 * r768608;
        double r768610 = r768607 * r768609;
        double r768611 = r768604 * r768610;
        double r768612 = z;
        double r768613 = sin(r768602);
        double r768614 = r768612 * r768613;
        double r768615 = r768611 - r768614;
        return r768615;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot x\right) \cdot \sqrt[3]{\cos y}\right)} \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.4

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

  8. Final simplification0.4

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

Reproduce

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