Average Error: 0.1 → 0.1
Time: 18.6s
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 r9926510 = x;
        double r9926511 = y;
        double r9926512 = cos(r9926511);
        double r9926513 = r9926510 * r9926512;
        double r9926514 = z;
        double r9926515 = sin(r9926511);
        double r9926516 = r9926514 * r9926515;
        double r9926517 = r9926513 - r9926516;
        return r9926517;
}
↓
double f(double x, double y, double z) {
        double r9926518 = x;
        double r9926519 = y;
        double r9926520 = cos(r9926519);
        double r9926521 = r9926518 * r9926520;
        double r9926522 = z;
        double r9926523 = sin(r9926519);
        double r9926524 = r9926522 * r9926523;
        double r9926525 = r9926521 - r9926524;
        return r9926525;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))