Average Error: 0.1 → 0.4
Time: 11.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r269417 = x;
        double r269418 = y;
        double r269419 = cos(r269418);
        double r269420 = r269417 * r269419;
        double r269421 = z;
        double r269422 = sin(r269418);
        double r269423 = r269421 * r269422;
        double r269424 = r269420 - r269423;
        return r269424;
}
↓
double f(double x, double y, double z) {
        double r269425 = x;
        double r269426 = y;
        double r269427 = cos(r269426);
        double r269428 = cbrt(r269427);
        double r269429 = r269428 * r269428;
        double r269430 = r269425 * r269429;
        double r269431 = r269430 * r269428;
        double r269432 = z;
        double r269433 = sin(r269426);
        double r269434 = r269432 * r269433;
        double r269435 = r269431 - r269434;
        return r269435;
}

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

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))