Average Error: 0.0 → 0.4
Time: 5.3s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r219619 = x;
        double r219620 = y;
        double r219621 = cos(r219620);
        double r219622 = r219619 + r219621;
        double r219623 = z;
        double r219624 = sin(r219620);
        double r219625 = r219623 * r219624;
        double r219626 = r219622 - r219625;
        return r219626;
}
↓
double f(double x, double y, double z) {
        double r219627 = x;
        double r219628 = y;
        double r219629 = cos(r219628);
        double r219630 = r219627 + r219629;
        double r219631 = z;
        double r219632 = sin(r219628);
        double r219633 = cbrt(r219632);
        double r219634 = r219633 * r219633;
        double r219635 = r219631 * r219634;
        double r219636 = r219635 * r219633;
        double r219637 = r219630 - r219636;
        return r219637;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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-cbrt0.4

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020021 
(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))))