Average Error: 0.1 → 0.3
Time: 18.0s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) - \sin y \cdot z
double f(double x, double y, double z) {
        double r11118602 = x;
        double r11118603 = y;
        double r11118604 = cos(r11118603);
        double r11118605 = r11118602 * r11118604;
        double r11118606 = z;
        double r11118607 = sin(r11118603);
        double r11118608 = r11118606 * r11118607;
        double r11118609 = r11118605 - r11118608;
        return r11118609;
}
↓
double f(double x, double y, double z) {
        double r11118610 = y;
        double r11118611 = cos(r11118610);
        double r11118612 = cbrt(r11118611);
        double r11118613 = r11118612 * r11118612;
        double r11118614 = cbrt(r11118613);
        double r11118615 = cbrt(r11118612);
        double r11118616 = r11118614 * r11118615;
        double r11118617 = r11118611 * r11118611;
        double r11118618 = 0.3333333333333333;
        double r11118619 = pow(r11118617, r11118618);
        double r11118620 = x;
        double r11118621 = r11118619 * r11118620;
        double r11118622 = r11118616 * r11118621;
        double r11118623 = sin(r11118610);
        double r11118624 = z;
        double r11118625 = r11118623 * r11118624;
        double r11118626 = r11118622 - r11118625;
        return r11118626;
}

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

    \[x \cdot \cos y - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.4

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  7. Applied pow1/316.4

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  8. Applied pow-prod-down0.2

    \[\leadsto \left(x \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.3

    \[\leadsto \left(x \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}}} - z \cdot \sin y\]

  11. Applied cbrt-prod0.3

    \[\leadsto \left(x \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)} - z \cdot \sin y\]

  12. Final simplification0.3

    \[\leadsto \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) - \sin y \cdot z\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))