Average Error: 0.1 → 0.2
Time: 23.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}} \cdot \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}}\right)\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}} \cdot \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}}\right)\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r11557445 = x;
        double r11557446 = y;
        double r11557447 = sin(r11557446);
        double r11557448 = r11557445 * r11557447;
        double r11557449 = z;
        double r11557450 = cos(r11557446);
        double r11557451 = r11557449 * r11557450;
        double r11557452 = r11557448 + r11557451;
        return r11557452;
}
↓
double f(double x, double y, double z) {
        double r11557453 = y;
        double r11557454 = cos(r11557453);
        double r11557455 = cbrt(r11557454);
        double r11557456 = r11557454 * r11557454;
        double r11557457 = 0.16666666666666666;
        double r11557458 = pow(r11557456, r11557457);
        double r11557459 = z;
        double r11557460 = r11557459 * r11557458;
        double r11557461 = r11557458 * r11557460;
        double r11557462 = r11557455 * r11557461;
        double r11557463 = x;
        double r11557464 = sin(r11557453);
        double r11557465 = r11557463 * r11557464;
        double r11557466 = r11557462 + r11557465;
        return r11557466;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Using strategy rm

  6. Applied pow1/315.4

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

  7. Applied pow1/315.4

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

  8. Applied pow-prod-down0.2

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

  10. Applied sqr-pow0.2

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

  11. Applied associate-*r*0.2

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

  12. Final simplification0.2

    \[\leadsto \sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}} \cdot \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}}\right)\right) + x \cdot \sin y\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))