Average Error: 0.1 → 0.0
Time: 10.8s
Precision: binary64
\[\left(x + \sin y\right) + z \cdot \cos y \]
↓
\[\mathsf{fma}\left(z, \cos y, x + \sin y\right) \]
\left(x + \sin y\right) + z \cdot \cos y
↓
\mathsf{fma}\left(z, \cos y, x + \sin y\right)

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))
↓
(FPCore (x y z) :precision binary64 (fma z (cos y) (+ x (sin y))))
double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}
↓
double code(double x, double y, double z) {
	return fma(z, cos(y), (x + sin(y)));
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021275 
(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))))