Average Error: 0.1 → 0.4
Time: 4.9s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r149218 = x;
        double r149219 = y;
        double r149220 = cos(r149219);
        double r149221 = r149218 + r149220;
        double r149222 = z;
        double r149223 = sin(r149219);
        double r149224 = r149222 * r149223;
        double r149225 = r149221 - r149224;
        return r149225;
}
↓
double f(double x, double y, double z) {
        double r149226 = x;
        double r149227 = y;
        double r149228 = cos(r149227);
        double r149229 = r149226 + r149228;
        double r149230 = z;
        double r149231 = sin(r149227);
        double r149232 = r149230 * r149231;
        double r149233 = cbrt(r149232);
        double r149234 = cbrt(r149230);
        double r149235 = r149233 * r149234;
        double r149236 = cbrt(r149231);
        double r149237 = r149236 * r149236;
        double r149238 = cbrt(r149237);
        double r149239 = cbrt(r149236);
        double r149240 = r149238 * r149239;
        double r149241 = r149235 * r149240;
        double r149242 = r149241 * r149233;
        double r149243 = r149229 - r149242;
        return r149243;
}

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

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

  6. Applied associate-*r*0.3

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

  8. Applied add-cube-cbrt0.3

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

  9. Applied cbrt-prod0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020036 +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))))