Average Error: 0.1 → 0.3
Time: 16.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r145345 = x;
        double r145346 = y;
        double r145347 = cos(r145346);
        double r145348 = r145345 * r145347;
        double r145349 = z;
        double r145350 = sin(r145346);
        double r145351 = r145349 * r145350;
        double r145352 = r145348 - r145351;
        return r145352;
}
↓
double f(double x, double y, double z) {
        double r145353 = x;
        double r145354 = y;
        double r145355 = cos(r145354);
        double r145356 = 2.0;
        double r145357 = pow(r145355, r145356);
        double r145358 = 0.6666666666666666;
        double r145359 = pow(r145357, r145358);
        double r145360 = cbrt(r145359);
        double r145361 = r145353 * r145360;
        double r145362 = cbrt(r145357);
        double r145363 = 0.3333333333333333;
        double r145364 = pow(r145362, r145363);
        double r145365 = r145361 * r145364;
        double r145366 = cbrt(r145355);
        double r145367 = r145365 * r145366;
        double r145368 = z;
        double r145369 = sin(r145354);
        double r145370 = r145368 * r145369;
        double r145371 = r145367 - r145370;
        return r145371;
}

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 pow1/315.6

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

  7. Applied pow1/315.6

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

  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. Simplified0.2

    \[\leadsto \left(x \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  10. Using strategy rm

  11. Applied add-cube-cbrt0.3

    \[\leadsto \left(x \cdot {\color{blue}{\left(\left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  12. Applied unpow-prod-down0.3

    \[\leadsto \left(x \cdot \color{blue}{\left({\left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}} \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right)}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  13. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right)} \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  14. Simplified0.3

    \[\leadsto \left(\color{blue}{\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right)} \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  15. Final simplification0.3

    \[\leadsto \left(\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))