Average Error: 0.1 → 0.2
Time: 4.7s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r160330 = x;
        double r160331 = y;
        double r160332 = cos(r160331);
        double r160333 = r160330 * r160332;
        double r160334 = z;
        double r160335 = sin(r160331);
        double r160336 = r160334 * r160335;
        double r160337 = r160333 - r160336;
        return r160337;
}
↓
double f(double x, double y, double z) {
        double r160338 = x;
        double r160339 = y;
        double r160340 = cos(r160339);
        double r160341 = 2.0;
        double r160342 = pow(r160340, r160341);
        double r160343 = log(r160342);
        double r160344 = exp(r160343);
        double r160345 = 0.3333333333333333;
        double r160346 = pow(r160344, r160345);
        double r160347 = r160338 * r160346;
        double r160348 = cbrt(r160340);
        double r160349 = r160347 * r160348;
        double r160350 = z;
        double r160351 = sin(r160339);
        double r160352 = r160350 * r160351;
        double r160353 = r160349 - r160352;
        return r160353;
}

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 pow1/316.1

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

  7. Applied pow1/316.1

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

  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-exp-log16.1

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

  12. Applied pow-exp16.1

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))