Average Error: 0.0 → 0.3
Time: 14.4s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r138020 = x;
        double r138021 = y;
        double r138022 = cos(r138021);
        double r138023 = r138020 + r138022;
        double r138024 = z;
        double r138025 = sin(r138021);
        double r138026 = r138024 * r138025;
        double r138027 = r138023 - r138026;
        return r138027;
}
↓
double f(double x, double y, double z) {
        double r138028 = x;
        double r138029 = y;
        double r138030 = cos(r138029);
        double r138031 = r138028 + r138030;
        double r138032 = z;
        double r138033 = cbrt(r138032);
        double r138034 = sin(r138029);
        double r138035 = cbrt(r138034);
        double r138036 = r138033 * r138035;
        double r138037 = r138032 * r138034;
        double r138038 = cbrt(r138037);
        double r138039 = r138036 * r138038;
        double r138040 = r138039 * r138038;
        double r138041 = r138031 - r138040;
        return r138041;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt0.3

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

  5. Applied cbrt-prod0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))