Average Error: 0.1 → 0.2
Time: 21.6s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \left(\left(\cos y \cdot \cos y\right) \cdot \left(\cos y \cdot \cos y\right)\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \left(\left(\cos y \cdot \cos y\right) \cdot \left(\cos y \cdot \cos y\right)\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z
double f(double x, double y, double z) {
        double r9502560 = x;
        double r9502561 = y;
        double r9502562 = cos(r9502561);
        double r9502563 = r9502560 * r9502562;
        double r9502564 = z;
        double r9502565 = sin(r9502561);
        double r9502566 = r9502564 * r9502565;
        double r9502567 = r9502563 - r9502566;
        return r9502567;
}
↓
double f(double x, double y, double z) {
        double r9502568 = x;
        double r9502569 = y;
        double r9502570 = cos(r9502569);
        double r9502571 = r9502570 * r9502570;
        double r9502572 = r9502571 * r9502571;
        double r9502573 = r9502571 * r9502572;
        double r9502574 = cbrt(r9502573);
        double r9502575 = 0.3333333333333333;
        double r9502576 = pow(r9502574, r9502575);
        double r9502577 = r9502568 * r9502576;
        double r9502578 = cbrt(r9502570);
        double r9502579 = r9502577 * r9502578;
        double r9502580 = sin(r9502569);
        double r9502581 = z;
        double r9502582 = r9502580 * r9502581;
        double r9502583 = r9502579 - r9502582;
        return r9502583;
}

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 pow1/316.3

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

  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-cbrt-cube0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))