Average Error: 0.1 → 0.1
Time: 19.7s
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 r12767254 = x;
        double r12767255 = y;
        double r12767256 = cos(r12767255);
        double r12767257 = r12767254 * r12767256;
        double r12767258 = z;
        double r12767259 = sin(r12767255);
        double r12767260 = r12767258 * r12767259;
        double r12767261 = r12767257 - r12767260;
        return r12767261;
}
↓
double f(double x, double y, double z) {
        double r12767262 = x;
        double r12767263 = y;
        double r12767264 = cos(r12767263);
        double r12767265 = r12767262 * r12767264;
        double r12767266 = z;
        double r12767267 = sin(r12767263);
        double r12767268 = r12767266 * r12767267;
        double r12767269 = r12767265 - r12767268;
        return r12767269;
}

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))))