Average Error: 0.1 → 0.3
Time: 15.9s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right)\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left(z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right)\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r181462 = x;
        double r181463 = y;
        double r181464 = sin(r181463);
        double r181465 = r181462 * r181464;
        double r181466 = z;
        double r181467 = cos(r181463);
        double r181468 = r181466 * r181467;
        double r181469 = r181465 + r181468;
        return r181469;
}
↓
double f(double x, double y, double z) {
        double r181470 = y;
        double r181471 = cos(r181470);
        double r181472 = cbrt(r181471);
        double r181473 = z;
        double r181474 = 2.0;
        double r181475 = pow(r181471, r181474);
        double r181476 = 0.1111111111111111;
        double r181477 = pow(r181475, r181476);
        double r181478 = 0.6666666666666666;
        double r181479 = pow(r181475, r181478);
        double r181480 = cbrt(r181479);
        double r181481 = r181477 * r181480;
        double r181482 = r181473 * r181481;
        double r181483 = r181472 * r181482;
        double r181484 = x;
        double r181485 = sin(r181470);
        double r181486 = r181484 * r181485;
        double r181487 = r181483 + r181486;
        return r181487;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

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

  7. Applied cbrt-unprod0.3

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

  8. Simplified0.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Applied cbrt-prod0.4

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

  12. Simplified0.3

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

  13. Taylor expanded around inf 0.3

    \[\leadsto x \cdot \sin y + \left(\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}} \cdot \color{blue}{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{9}}}\right) \cdot z\right) \cdot \sqrt[3]{\cos y}\]

  14. Final simplification0.3

    \[\leadsto \sqrt[3]{\cos y} \cdot \left(z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right)\right) + x \cdot \sin y\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))