Average Error: 0.1 → 0.3
Time: 5.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r160451 = x;
        double r160452 = y;
        double r160453 = cos(r160452);
        double r160454 = r160451 * r160453;
        double r160455 = z;
        double r160456 = sin(r160452);
        double r160457 = r160455 * r160456;
        double r160458 = r160454 + r160457;
        return r160458;
}
↓
double f(double x, double y, double z) {
        double r160459 = x;
        double r160460 = y;
        double r160461 = cos(r160460);
        double r160462 = 2.0;
        double r160463 = pow(r160461, r160462);
        double r160464 = cbrt(r160463);
        double r160465 = log1p(r160464);
        double r160466 = expm1(r160465);
        double r160467 = r160459 * r160466;
        double r160468 = cbrt(r160461);
        double r160469 = r160467 * r160468;
        double r160470 = z;
        double r160471 = sin(r160460);
        double r160472 = r160470 * r160471;
        double r160473 = r160469 + r160472;
        return r160473;
}

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 expm1-log1p-u0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))