Average Error: 0.1 → 0.0
Time: 34.1s
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 r8128149 = x;
        double r8128150 = y;
        double r8128151 = sin(r8128150);
        double r8128152 = r8128149 + r8128151;
        double r8128153 = z;
        double r8128154 = cos(r8128150);
        double r8128155 = r8128153 * r8128154;
        double r8128156 = r8128152 + r8128155;
        return r8128156;
}
↓
double f(double x, double y, double z) {
        double r8128157 = y;
        double r8128158 = cos(r8128157);
        double r8128159 = z;
        double r8128160 = x;
        double r8128161 = sin(r8128157);
        double r8128162 = r8128160 + r8128161;
        double r8128163 = fma(r8128158, r8128159, r8128162);
        return r8128163;
}

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 2019168 +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))))