Average Error: 0.1 → 0.3
Time: 13.0s
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 r217380 = x;
        double r217381 = y;
        double r217382 = cos(r217381);
        double r217383 = r217380 * r217382;
        double r217384 = z;
        double r217385 = sin(r217381);
        double r217386 = r217384 * r217385;
        double r217387 = r217383 + r217386;
        return r217387;
}
↓
double f(double x, double y, double z) {
        double r217388 = x;
        double r217389 = y;
        double r217390 = cos(r217389);
        double r217391 = 2.0;
        double r217392 = pow(r217390, r217391);
        double r217393 = 0.6666666666666666;
        double r217394 = pow(r217392, r217393);
        double r217395 = 0.3333333333333333;
        double r217396 = pow(r217392, r217395);
        double r217397 = r217394 * r217396;
        double r217398 = cbrt(r217397);
        double r217399 = r217388 * r217398;
        double r217400 = cbrt(r217390);
        double r217401 = r217399 * r217400;
        double r217402 = z;
        double r217403 = sin(r217389);
        double r217404 = r217402 * r217403;
        double r217405 = r217401 + r217404;
        return r217405;
}

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. Using strategy rm

  12. Applied pow1/30.3

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

  13. 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 2020047 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))