Average Error: 0.1 → 0.2
Time: 15.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r154261 = x;
        double r154262 = y;
        double r154263 = cos(r154262);
        double r154264 = r154261 * r154263;
        double r154265 = z;
        double r154266 = sin(r154262);
        double r154267 = r154265 * r154266;
        double r154268 = r154264 - r154267;
        return r154268;
}
↓
double f(double x, double y, double z) {
        double r154269 = x;
        double r154270 = y;
        double r154271 = cos(r154270);
        double r154272 = 2.0;
        double r154273 = pow(r154271, r154272);
        double r154274 = 0.3333333333333333;
        double r154275 = pow(r154273, r154274);
        double r154276 = r154269 * r154275;
        double r154277 = cbrt(r154271);
        double r154278 = exp(r154277);
        double r154279 = log(r154278);
        double r154280 = r154276 * r154279;
        double r154281 = z;
        double r154282 = sin(r154270);
        double r154283 = r154281 * r154282;
        double r154284 = r154280 - r154283;
        return r154284;
}

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 pow1/315.9

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

  7. Applied pow1/315.9

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

  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-log-exp0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 
(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))))