Average Error: 0.1 → 0.1
Time: 17.0s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x + \sin y\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x + \sin y\right)
double f(double x, double y, double z) {
        double r8721462 = x;
        double r8721463 = y;
        double r8721464 = sin(r8721463);
        double r8721465 = r8721462 + r8721464;
        double r8721466 = z;
        double r8721467 = cos(r8721463);
        double r8721468 = r8721466 * r8721467;
        double r8721469 = r8721465 + r8721468;
        return r8721469;
}
↓
double f(double x, double y, double z) {
        double r8721470 = y;
        double r8721471 = cos(r8721470);
        double r8721472 = z;
        double r8721473 = x;
        double r8721474 = sin(r8721470);
        double r8721475 = r8721473 + r8721474;
        double r8721476 = fma(r8721471, r8721472, r8721475);
        return r8721476;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x + \sin y\right) + z \cdot \cos y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))