Average Error: 0.1 → 0.6
Time: 22.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r8178407 = x;
        double r8178408 = y;
        double r8178409 = cos(r8178408);
        double r8178410 = r8178407 * r8178409;
        double r8178411 = z;
        double r8178412 = sin(r8178408);
        double r8178413 = r8178411 * r8178412;
        double r8178414 = r8178410 - r8178413;
        return r8178414;
}
↓
double f(double x, double y, double z) {
        double r8178415 = x;
        double r8178416 = y;
        double r8178417 = cos(r8178416);
        double r8178418 = r8178415 * r8178417;
        double r8178419 = z;
        double r8178420 = cbrt(r8178419);
        double r8178421 = r8178420 * r8178420;
        double r8178422 = sin(r8178416);
        double r8178423 = r8178422 * r8178420;
        double r8178424 = r8178421 * r8178423;
        double r8178425 = r8178418 - r8178424;
        return r8178425;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))