Average Error: 0.1 → 0.3
Time: 4.8s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\left(x \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\left(x \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left({\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 r269281 = x;
        double r269282 = y;
        double r269283 = cos(r269282);
        double r269284 = r269281 * r269283;
        double r269285 = z;
        double r269286 = sin(r269282);
        double r269287 = r269285 * r269286;
        double r269288 = r269284 + r269287;
        return r269288;
}
↓
double f(double x, double y, double z) {
        double r269289 = x;
        double r269290 = y;
        double r269291 = cos(r269290);
        double r269292 = 2.0;
        double r269293 = pow(r269291, r269292);
        double r269294 = 0.3333333333333333;
        double r269295 = pow(r269293, r269294);
        double r269296 = sqrt(r269295);
        double r269297 = r269289 * r269296;
        double r269298 = r269297 * r269296;
        double r269299 = cbrt(r269291);
        double r269300 = r269298 * r269299;
        double r269301 = z;
        double r269302 = sin(r269290);
        double r269303 = r269301 * r269302;
        double r269304 = r269300 + r269303;
        return r269304;
}

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-sqr-sqrt0.2

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

  12. Applied associate-*r*0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))