Average Error: 0.1 → 0.3
Time: 44.1s
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 r13291002 = x;
        double r13291003 = y;
        double r13291004 = sin(r13291003);
        double r13291005 = r13291002 * r13291004;
        double r13291006 = z;
        double r13291007 = cos(r13291003);
        double r13291008 = r13291006 * r13291007;
        double r13291009 = r13291005 + r13291008;
        return r13291009;
}
↓
double f(double x, double y, double z) {
        double r13291010 = y;
        double r13291011 = cos(r13291010);
        double r13291012 = cbrt(r13291011);
        double r13291013 = r13291011 * r13291011;
        double r13291014 = cbrt(r13291013);
        double r13291015 = z;
        double r13291016 = r13291014 * r13291015;
        double r13291017 = r13291012 * r13291016;
        double r13291018 = x;
        double r13291019 = sin(r13291010);
        double r13291020 = r13291018 * r13291019;
        double r13291021 = r13291017 + r13291020;
        return r13291021;
}

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))))