Average Error: 0.1 → 0.4
Time: 21.5s
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 r120496 = x;
        double r120497 = y;
        double r120498 = cos(r120497);
        double r120499 = r120496 + r120498;
        double r120500 = z;
        double r120501 = sin(r120497);
        double r120502 = r120500 * r120501;
        double r120503 = r120499 - r120502;
        return r120503;
}
↓
double f(double x, double y, double z) {
        double r120504 = x;
        double r120505 = y;
        double r120506 = cos(r120505);
        double r120507 = r120504 + r120506;
        double r120508 = z;
        double r120509 = cbrt(r120508);
        double r120510 = r120509 * r120509;
        double r120511 = sin(r120505);
        double r120512 = r120509 * r120511;
        double r120513 = r120510 * r120512;
        double r120514 = r120507 - r120513;
        return r120514;
}

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 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  (- (+ x (cos y)) (* z (sin y))))