Average Error: 0.1 → 0.2
Time: 5.0s
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 r284268 = x;
        double r284269 = y;
        double r284270 = cos(r284269);
        double r284271 = r284268 * r284270;
        double r284272 = z;
        double r284273 = sin(r284269);
        double r284274 = r284272 * r284273;
        double r284275 = r284271 - r284274;
        return r284275;
}
↓
double f(double x, double y, double z) {
        double r284276 = x;
        double r284277 = y;
        double r284278 = cos(r284277);
        double r284279 = 2.0;
        double r284280 = pow(r284278, r284279);
        double r284281 = log(r284280);
        double r284282 = exp(r284281);
        double r284283 = 0.3333333333333333;
        double r284284 = pow(r284282, r284283);
        double r284285 = r284276 * r284284;
        double r284286 = cbrt(r284278);
        double r284287 = r284285 * r284286;
        double r284288 = z;
        double r284289 = sin(r284277);
        double r284290 = r284288 * r284289;
        double r284291 = r284287 - r284290;
        return r284291;
}

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 pow1/316.3

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

  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. 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-log16.3

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

  12. Applied pow-exp16.3

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

  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 2020065 
(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))))