Average Error: 0.0 → 0.0
Time: 954.0ms
Precision: binary64
\[x - y \cdot y \]
↓
\[\left(x - y \cdot y\right) + \mathsf{fma}\left(-y, y, y \cdot y\right) \]
x - y \cdot y
↓
\left(x - y \cdot y\right) + \mathsf{fma}\left(-y, y, y \cdot y\right)

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

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x - y \cdot y \]

  2. Applied *-un-lft-identity_binary640.0

    \[\leadsto \color{blue}{1 \cdot x} - y \cdot y \]

  3. Applied prod-diff_binary640.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, -y \cdot y\right) + \mathsf{fma}\left(-y, y, y \cdot y\right)} \]

  4. Applied fma-udef_binary640.0

    \[\leadsto \color{blue}{\left(1 \cdot x + \left(-y \cdot y\right)\right)} + \mathsf{fma}\left(-y, y, y \cdot y\right) \]

  5. Simplified0.0

    \[\leadsto \left(\color{blue}{x} + \left(-y \cdot y\right)\right) + \mathsf{fma}\left(-y, y, y \cdot y\right) \]

  6. Final simplification0.0

    \[\leadsto \left(x - y \cdot y\right) + \mathsf{fma}\left(-y, y, y \cdot y\right) \]

Reproduce

herbie shell --seed 2021313 
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))