Average Error: 0.1 → 0.1
Time: 22.1s
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 r10928436 = x;
        double r10928437 = y;
        double r10928438 = cos(r10928437);
        double r10928439 = r10928436 * r10928438;
        double r10928440 = z;
        double r10928441 = sin(r10928437);
        double r10928442 = r10928440 * r10928441;
        double r10928443 = r10928439 + r10928442;
        return r10928443;
}
↓
double f(double x, double y, double z) {
        double r10928444 = y;
        double r10928445 = sin(r10928444);
        double r10928446 = z;
        double r10928447 = x;
        double r10928448 = cos(r10928444);
        double r10928449 = r10928447 * r10928448;
        double r10928450 = fma(r10928445, r10928446, r10928449);
        return r10928450;
}

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 2019163 +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))))