Average Error: 0.1 → 0.4
Time: 23.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(-z\right) \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\left(-z\right) \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right)
double f(double x, double y, double z) {
        double r12493443 = x;
        double r12493444 = y;
        double r12493445 = cos(r12493444);
        double r12493446 = r12493443 * r12493445;
        double r12493447 = z;
        double r12493448 = sin(r12493444);
        double r12493449 = r12493447 * r12493448;
        double r12493450 = r12493446 - r12493449;
        return r12493450;
}
↓
double f(double x, double y, double z) {
        double r12493451 = z;
        double r12493452 = -r12493451;
        double r12493453 = y;
        double r12493454 = sin(r12493453);
        double r12493455 = r12493452 * r12493454;
        double r12493456 = cos(r12493453);
        double r12493457 = cbrt(r12493456);
        double r12493458 = r12493457 * r12493457;
        double r12493459 = x;
        double r12493460 = r12493458 * r12493459;
        double r12493461 = r12493457 * r12493460;
        double r12493462 = r12493455 + r12493461;
        return r12493462;
}

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 sub-neg0.1

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

  5. Applied add-cube-cbrt0.4

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

  6. Applied associate-*r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))