Average Error: 0.1 → 0.0
Time: 14.8s
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 r88122 = x;
        double r88123 = y;
        double r88124 = sin(r88123);
        double r88125 = r88122 + r88124;
        double r88126 = z;
        double r88127 = cos(r88123);
        double r88128 = r88126 * r88127;
        double r88129 = r88125 + r88128;
        return r88129;
}
↓
double f(double x, double y, double z) {
        double r88130 = y;
        double r88131 = cos(r88130);
        double r88132 = z;
        double r88133 = x;
        double r88134 = sin(r88130);
        double r88135 = r88133 + r88134;
        double r88136 = fma(r88131, r88132, r88135);
        return r88136;
}

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 2019198 +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))))