Average Error: 0.1 → 0.1
Time: 5.4s
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 r187560 = x;
        double r187561 = y;
        double r187562 = sin(r187561);
        double r187563 = r187560 + r187562;
        double r187564 = z;
        double r187565 = cos(r187561);
        double r187566 = r187564 * r187565;
        double r187567 = r187563 + r187566;
        return r187567;
}
↓
double f(double x, double y, double z) {
        double r187568 = y;
        double r187569 = cos(r187568);
        double r187570 = z;
        double r187571 = x;
        double r187572 = sin(r187568);
        double r187573 = r187571 + r187572;
        double r187574 = fma(r187569, r187570, r187573);
        return r187574;
}

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 2020021 +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))))