Average Error: 0.1 → 0.1
Time: 8.8s
Precision: binary64
\[\left(x + \sin y\right) + z \cdot \cos y \]
↓
\[x + \mathsf{fma}\left(\cos y, z, \sin y\right) \]
\left(x + \sin y\right) + z \cdot \cos y
↓
x + \mathsf{fma}\left(\cos y, z, \sin y\right)

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))
↓
(FPCore (x y z) :precision binary64 (+ x (fma (cos y) z (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 x + fma(cos(y), z, 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. Applied associate-+l+_binary640.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021224 
(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))))