Average Error: 0.1 → 0.1
Time: 24.1s
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 r10516497 = x;
        double r10516498 = y;
        double r10516499 = cos(r10516498);
        double r10516500 = r10516497 * r10516499;
        double r10516501 = z;
        double r10516502 = sin(r10516498);
        double r10516503 = r10516501 * r10516502;
        double r10516504 = r10516500 + r10516503;
        return r10516504;
}
↓
double f(double x, double y, double z) {
        double r10516505 = y;
        double r10516506 = sin(r10516505);
        double r10516507 = z;
        double r10516508 = x;
        double r10516509 = cos(r10516505);
        double r10516510 = r10516508 * r10516509;
        double r10516511 = fma(r10516506, r10516507, r10516510);
        return r10516511;
}

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