Average Error: 0.1 → 0.2
Time: 4.4s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(z \cdot \left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y}\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(z \cdot \left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r176680 = x;
        double r176681 = y;
        double r176682 = sin(r176681);
        double r176683 = r176680 + r176682;
        double r176684 = z;
        double r176685 = cos(r176681);
        double r176686 = r176684 * r176685;
        double r176687 = r176683 + r176686;
        return r176687;
}
↓
double f(double x, double y, double z) {
        double r176688 = x;
        double r176689 = y;
        double r176690 = sin(r176689);
        double r176691 = r176688 + r176690;
        double r176692 = z;
        double r176693 = cos(r176689);
        double r176694 = 2.0;
        double r176695 = pow(r176693, r176694);
        double r176696 = cbrt(r176695);
        double r176697 = sqrt(r176696);
        double r176698 = r176697 * r176697;
        double r176699 = r176692 * r176698;
        double r176700 = cbrt(r176693);
        double r176701 = r176699 * r176700;
        double r176702 = r176691 + r176701;
        return r176702;
}

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

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

  3. Applied add-cube-cbrt0.2

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

  4. Applied associate-*r*0.3

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

  6. Applied cbrt-unprod0.2

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

  7. Simplified0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \color{blue}{\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)}\right) \cdot \sqrt[3]{\cos y}\]

  10. Final simplification0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))