Average Error: 0.1 → 0.1
Time: 20.9s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[z \cdot \sin y + x \cdot \cos y\]
x \cdot \cos y + z \cdot \sin y
↓
z \cdot \sin y + x \cdot \cos y
double f(double x, double y, double z) {
        double r9962715 = x;
        double r9962716 = y;
        double r9962717 = cos(r9962716);
        double r9962718 = r9962715 * r9962717;
        double r9962719 = z;
        double r9962720 = sin(r9962716);
        double r9962721 = r9962719 * r9962720;
        double r9962722 = r9962718 + r9962721;
        return r9962722;
}
↓
double f(double x, double y, double z) {
        double r9962723 = z;
        double r9962724 = y;
        double r9962725 = sin(r9962724);
        double r9962726 = r9962723 * r9962725;
        double r9962727 = x;
        double r9962728 = cos(r9962724);
        double r9962729 = r9962727 * r9962728;
        double r9962730 = r9962726 + r9962729;
        return r9962730;
}

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

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

  4. Final simplification0.1

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

Reproduce

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