Average Error: 0.1 → 0.0
Time: 58.4s
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 r10605619 = x;
        double r10605620 = y;
        double r10605621 = sin(r10605620);
        double r10605622 = r10605619 + r10605621;
        double r10605623 = z;
        double r10605624 = cos(r10605620);
        double r10605625 = r10605623 * r10605624;
        double r10605626 = r10605622 + r10605625;
        return r10605626;
}
↓
double f(double x, double y, double z) {
        double r10605627 = y;
        double r10605628 = cos(r10605627);
        double r10605629 = z;
        double r10605630 = x;
        double r10605631 = sin(r10605627);
        double r10605632 = r10605630 + r10605631;
        double r10605633 = fma(r10605628, r10605629, r10605632);
        return r10605633;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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))))