Average Error: 0.1 → 0.3
Time: 5.0s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)
double f(double x, double y, double z) {
        double r179207 = x;
        double r179208 = y;
        double r179209 = cos(r179208);
        double r179210 = r179207 + r179209;
        double r179211 = z;
        double r179212 = sin(r179208);
        double r179213 = r179211 * r179212;
        double r179214 = r179210 - r179213;
        return r179214;
}
↓
double f(double x, double y, double z) {
        double r179215 = x;
        double r179216 = y;
        double r179217 = cos(r179216);
        double r179218 = r179215 + r179217;
        double r179219 = z;
        double r179220 = sin(r179216);
        double r179221 = r179219 * r179220;
        double r179222 = cbrt(r179221);
        double r179223 = r179222 * r179222;
        double r179224 = cbrt(r179219);
        double r179225 = cbrt(r179220);
        double r179226 = r179224 * r179225;
        double r179227 = r179223 * r179226;
        double r179228 = r179218 - r179227;
        return r179228;
}

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 0.1

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  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

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020027 +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))))