Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)
double f(double x, double y, double z) {
        double r217376 = x;
        double r217377 = y;
        double r217378 = sin(r217377);
        double r217379 = r217376 * r217378;
        double r217380 = z;
        double r217381 = cos(r217377);
        double r217382 = r217380 * r217381;
        double r217383 = r217379 + r217382;
        return r217383;
}
↓
double f(double x, double y, double z) {
        double r217384 = x;
        double r217385 = y;
        double r217386 = sin(r217385);
        double r217387 = z;
        double r217388 = cos(r217385);
        double r217389 = r217387 * r217388;
        double r217390 = fma(r217384, r217386, r217389);
        return r217390;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))