Average Error: 0.1 → 0.1
Time: 21.6s
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 r10295556 = x;
        double r10295557 = y;
        double r10295558 = cos(r10295557);
        double r10295559 = r10295556 * r10295558;
        double r10295560 = z;
        double r10295561 = sin(r10295557);
        double r10295562 = r10295560 * r10295561;
        double r10295563 = r10295559 + r10295562;
        return r10295563;
}
↓
double f(double x, double y, double z) {
        double r10295564 = y;
        double r10295565 = sin(r10295564);
        double r10295566 = z;
        double r10295567 = x;
        double r10295568 = cos(r10295564);
        double r10295569 = r10295567 * r10295568;
        double r10295570 = fma(r10295565, r10295566, r10295569);
        return r10295570;
}

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 2019164 +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))))