Average Error: 0.1 → 0.4
Time: 20.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r10079594 = x;
        double r10079595 = y;
        double r10079596 = cos(r10079595);
        double r10079597 = r10079594 * r10079596;
        double r10079598 = z;
        double r10079599 = sin(r10079595);
        double r10079600 = r10079598 * r10079599;
        double r10079601 = r10079597 + r10079600;
        return r10079601;
}
↓
double f(double x, double y, double z) {
        double r10079602 = y;
        double r10079603 = cos(r10079602);
        double r10079604 = cbrt(r10079603);
        double r10079605 = r10079604 * r10079604;
        double r10079606 = x;
        double r10079607 = r10079605 * r10079606;
        double r10079608 = r10079604 * r10079607;
        double r10079609 = z;
        double r10079610 = sin(r10079602);
        double r10079611 = r10079609 * r10079610;
        double r10079612 = r10079608 + r10079611;
        return r10079612;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))