Average Error: 0.1 → 0.4
Time: 6.3s
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 r155565 = x;
        double r155566 = y;
        double r155567 = cos(r155566);
        double r155568 = r155565 + r155567;
        double r155569 = z;
        double r155570 = sin(r155566);
        double r155571 = r155569 * r155570;
        double r155572 = r155568 - r155571;
        return r155572;
}
↓
double f(double x, double y, double z) {
        double r155573 = x;
        double r155574 = y;
        double r155575 = cos(r155574);
        double r155576 = r155573 + r155575;
        double r155577 = z;
        double r155578 = cbrt(r155577);
        double r155579 = r155578 * r155578;
        double r155580 = cbrt(r155579);
        double r155581 = r155578 * r155580;
        double r155582 = cbrt(r155578);
        double r155583 = r155581 * r155582;
        double r155584 = sin(r155574);
        double r155585 = r155578 * r155584;
        double r155586 = r155583 * r155585;
        double r155587 = r155576 - r155586;
        return r155587;
}

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))))