Average Error: 0.0 → 0.3
Time: 5.5s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(\left(\left(-{\left(\sqrt[3]{\sin y}\right)}^{3}\right) \cdot z + \cos y\right) + x\right) + z \cdot \left(\left(-\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{\sin y}\right) + {\left(\sqrt[3]{\sin y}\right)}^{3}\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(\left(\left(-{\left(\sqrt[3]{\sin y}\right)}^{3}\right) \cdot z + \cos y\right) + x\right) + z \cdot \left(\left(-\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{\sin y}\right) + {\left(\sqrt[3]{\sin y}\right)}^{3}\right)
double code(double x, double y, double z) {
	return ((x + cos(y)) - (z * sin(y)));
}
↓
double code(double x, double y, double z) {
	return ((((-pow(cbrt(sin(y)), 3.0) * z) + cos(y)) + x) + (z * (-((cbrt(sin(y)) * cbrt(sin(y))) * cbrt(sin(y))) + pow(cbrt(sin(y)), 3.0))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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

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

  4. Applied associate-*r*0.4

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

  5. Applied add-sqr-sqrt24.2

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

  6. Applied prod-diff24.2

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  10. Applied add-cbrt-cube0.4

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

  11. Applied rem-cube-cbrt0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020066 +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))))