Average Error: 0.0 → 0.0
Time: 8.7s
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 r210116 = x;
        double r210117 = y;
        double r210118 = sin(r210117);
        double r210119 = r210116 + r210118;
        double r210120 = z;
        double r210121 = cos(r210117);
        double r210122 = r210120 * r210121;
        double r210123 = r210119 + r210122;
        return r210123;
}
↓
double f(double x, double y, double z) {
        double r210124 = y;
        double r210125 = cos(r210124);
        double r210126 = z;
        double r210127 = x;
        double r210128 = sin(r210124);
        double r210129 = r210127 + r210128;
        double r210130 = fma(r210125, r210126, r210129);
        return r210130;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  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 2020045 +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))))