Average Error: 0.1 → 0.4
Time: 22.9s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r8290021 = x;
        double r8290022 = y;
        double r8290023 = cos(r8290022);
        double r8290024 = r8290021 + r8290023;
        double r8290025 = z;
        double r8290026 = sin(r8290022);
        double r8290027 = r8290025 * r8290026;
        double r8290028 = r8290024 - r8290027;
        return r8290028;
}
↓
double f(double x, double y, double z) {
        double r8290029 = x;
        double r8290030 = y;
        double r8290031 = cos(r8290030);
        double r8290032 = r8290029 + r8290031;
        double r8290033 = sin(r8290030);
        double r8290034 = z;
        double r8290035 = r8290033 * r8290034;
        double r8290036 = cbrt(r8290035);
        double r8290037 = cbrt(r8290033);
        double r8290038 = r8290037 * r8290037;
        double r8290039 = cbrt(r8290034);
        double r8290040 = r8290039 * r8290039;
        double r8290041 = r8290038 * r8290040;
        double r8290042 = r8290036 * r8290041;
        double r8290043 = r8290032 - r8290042;
        return r8290043;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

Enter valid numbers for all inputs

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

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

  5. Applied cbrt-prod0.3

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

  6. Applied cbrt-prod0.4

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

  7. Applied swap-sqr0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019162 +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))))