Average Error: 0.1 → 0.4
Time: 6.0s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r172647 = x;
        double r172648 = y;
        double r172649 = cos(r172648);
        double r172650 = r172647 + r172649;
        double r172651 = z;
        double r172652 = sin(r172648);
        double r172653 = r172651 * r172652;
        double r172654 = r172650 - r172653;
        return r172654;
}
↓
double f(double x, double y, double z) {
        double r172655 = x;
        double r172656 = y;
        double r172657 = cos(r172656);
        double r172658 = r172655 + r172657;
        double r172659 = z;
        double r172660 = cbrt(r172659);
        double r172661 = r172660 * r172660;
        double r172662 = cbrt(r172661);
        double r172663 = r172660 * r172662;
        double r172664 = cbrt(r172660);
        double r172665 = r172663 * r172664;
        double r172666 = sin(r172656);
        double r172667 = r172660 * r172666;
        double r172668 = r172665 * r172667;
        double r172669 = r172658 - r172668;
        return r172669;
}

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

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

  4. Applied associate-*l*0.4

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Applied associate-*r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 +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))))