Average Error: 0.1 → 0.1
Time: 21.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - z \cdot \sin y
double f(double x, double y, double z) {
        double r10291055 = x;
        double r10291056 = y;
        double r10291057 = cos(r10291056);
        double r10291058 = r10291055 * r10291057;
        double r10291059 = z;
        double r10291060 = sin(r10291056);
        double r10291061 = r10291059 * r10291060;
        double r10291062 = r10291058 - r10291061;
        return r10291062;
}
↓
double f(double x, double y, double z) {
        double r10291063 = x;
        double r10291064 = y;
        double r10291065 = cos(r10291064);
        double r10291066 = r10291063 * r10291065;
        double r10291067 = z;
        double r10291068 = sin(r10291064);
        double r10291069 = r10291067 * r10291068;
        double r10291070 = r10291066 - r10291069;
        return r10291070;
}

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 *-commutative0.1

    \[\leadsto \color{blue}{\cos y \cdot x} - z \cdot \sin y\]

  4. Final simplification0.1

    \[\leadsto x \cdot \cos y - z \cdot \sin y\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))