Average Error: 0.1 → 0.4
Time: 25.0s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r128601 = x;
        double r128602 = y;
        double r128603 = cos(r128602);
        double r128604 = r128601 + r128603;
        double r128605 = z;
        double r128606 = sin(r128602);
        double r128607 = r128605 * r128606;
        double r128608 = r128604 - r128607;
        return r128608;
}
↓
double f(double x, double y, double z) {
        double r128609 = x;
        double r128610 = y;
        double r128611 = cos(r128610);
        double r128612 = r128609 + r128611;
        double r128613 = z;
        double r128614 = cbrt(r128613);
        double r128615 = r128614 * r128614;
        double r128616 = sin(r128610);
        double r128617 = r128614 * r128616;
        double r128618 = r128615 * r128617;
        double r128619 = r128612 - r128618;
        return r128619;
}

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

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  (- (+ x (cos y)) (* z (sin y))))