Average Error: 0.1 → 0.1
Time: 17.1s
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 r8742212 = x;
        double r8742213 = y;
        double r8742214 = sin(r8742213);
        double r8742215 = r8742212 + r8742214;
        double r8742216 = z;
        double r8742217 = cos(r8742213);
        double r8742218 = r8742216 * r8742217;
        double r8742219 = r8742215 + r8742218;
        return r8742219;
}
↓
double f(double x, double y, double z) {
        double r8742220 = y;
        double r8742221 = cos(r8742220);
        double r8742222 = z;
        double r8742223 = x;
        double r8742224 = sin(r8742220);
        double r8742225 = r8742223 + r8742224;
        double r8742226 = fma(r8742221, r8742222, r8742225);
        return r8742226;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +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))))