Average Error: 0.1 → 0.1
Time: 26.4s
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 r12320321 = x;
        double r12320322 = y;
        double r12320323 = cos(r12320322);
        double r12320324 = r12320321 * r12320323;
        double r12320325 = z;
        double r12320326 = sin(r12320322);
        double r12320327 = r12320325 * r12320326;
        double r12320328 = r12320324 + r12320327;
        return r12320328;
}
↓
double f(double x, double y, double z) {
        double r12320329 = y;
        double r12320330 = sin(r12320329);
        double r12320331 = z;
        double r12320332 = x;
        double r12320333 = cos(r12320329);
        double r12320334 = r12320332 * r12320333;
        double r12320335 = fma(r12320330, r12320331, r12320334);
        return r12320335;
}

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 2019168 +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))))