Average Error: 0.1 → 0.3
Time: 4.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\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 r204386 = x;
        double r204387 = y;
        double r204388 = cos(r204387);
        double r204389 = r204386 * r204388;
        double r204390 = z;
        double r204391 = sin(r204387);
        double r204392 = r204390 * r204391;
        double r204393 = r204389 + r204392;
        return r204393;
}
↓
double f(double x, double y, double z) {
        double r204394 = x;
        double r204395 = y;
        double r204396 = cos(r204395);
        double r204397 = 2.0;
        double r204398 = pow(r204396, r204397);
        double r204399 = 0.6666666666666666;
        double r204400 = pow(r204398, r204399);
        double r204401 = 0.3333333333333333;
        double r204402 = pow(r204398, r204401);
        double r204403 = r204400 * r204402;
        double r204404 = cbrt(r204403);
        double r204405 = r204394 * r204404;
        double r204406 = cbrt(r204396);
        double r204407 = r204405 * r204406;
        double r204408 = z;
        double r204409 = sin(r204395);
        double r204410 = r204408 * r204409;
        double r204411 = r204407 + r204410;
        return r204411;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied add-cube-cbrt0.3

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

  10. Simplified0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020049 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))