Average Error: 0.1 → 0.0
Time: 4.4s
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 r162570 = x;
        double r162571 = y;
        double r162572 = sin(r162571);
        double r162573 = r162570 + r162572;
        double r162574 = z;
        double r162575 = cos(r162571);
        double r162576 = r162574 * r162575;
        double r162577 = r162573 + r162576;
        return r162577;
}
↓
double f(double x, double y, double z) {
        double r162578 = y;
        double r162579 = cos(r162578);
        double r162580 = z;
        double r162581 = x;
        double r162582 = sin(r162578);
        double r162583 = r162581 + r162582;
        double r162584 = fma(r162579, r162580, r162583);
        return r162584;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))