Average Error: 0.1 → 0.0
Time: 10.2s
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 r213082 = x;
        double r213083 = y;
        double r213084 = sin(r213083);
        double r213085 = r213082 + r213084;
        double r213086 = z;
        double r213087 = cos(r213083);
        double r213088 = r213086 * r213087;
        double r213089 = r213085 + r213088;
        return r213089;
}
↓
double f(double x, double y, double z) {
        double r213090 = y;
        double r213091 = cos(r213090);
        double r213092 = z;
        double r213093 = x;
        double r213094 = sin(r213090);
        double r213095 = r213093 + r213094;
        double r213096 = fma(r213091, r213092, r213095);
        return r213096;
}

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 2020046 +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))))