Average Error: 0.1 → 0.1
Time: 19.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r132503 = x;
        double r132504 = y;
        double r132505 = cos(r132504);
        double r132506 = r132503 * r132505;
        double r132507 = z;
        double r132508 = sin(r132504);
        double r132509 = r132507 * r132508;
        double r132510 = r132506 - r132509;
        return r132510;
}
↓
double f(double x, double y, double z) {
        double r132511 = y;
        double r132512 = sin(r132511);
        double r132513 = z;
        double r132514 = -r132513;
        double r132515 = x;
        double r132516 = cos(r132511);
        double r132517 = r132515 * r132516;
        double r132518 = fma(r132512, r132514, r132517);
        return r132518;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)\]

Reproduce

herbie shell --seed 2019179 +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))))