Average Error: 0.1 → 0.3
Time: 4.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\cos y\right)}^{2}\right)\right)}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\cos y\right)}^{2}\right)\right)}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r189458 = x;
        double r189459 = y;
        double r189460 = sin(r189459);
        double r189461 = r189458 * r189460;
        double r189462 = z;
        double r189463 = cos(r189459);
        double r189464 = r189462 * r189463;
        double r189465 = r189461 + r189464;
        return r189465;
}
↓
double f(double x, double y, double z) {
        double r189466 = x;
        double r189467 = y;
        double r189468 = sin(r189467);
        double r189469 = r189466 * r189468;
        double r189470 = z;
        double r189471 = cos(r189467);
        double r189472 = 2.0;
        double r189473 = pow(r189471, r189472);
        double r189474 = log1p(r189473);
        double r189475 = expm1(r189474);
        double r189476 = cbrt(r189475);
        double r189477 = r189470 * r189476;
        double r189478 = cbrt(r189471);
        double r189479 = r189477 * r189478;
        double r189480 = r189469 + r189479;
        return r189480;
}

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. Using strategy rm

  6. Applied cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied expm1-log1p-u0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\cos y\right)}^{2}\right)\right)}}\right) \cdot \sqrt[3]{\cos y}\]

  10. Final simplification0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\cos y\right)}^{2}\right)\right)}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))