Average Error: 0.0 → 0
Time: 371.0ms
Precision: 64
\[x \cdot x + 1\]
↓
\[\mathsf{fma}\left(x, x, 1\right)\]
x \cdot x + 1
↓
\mathsf{fma}\left(x, x, 1\right)
double code(double x) {
	return ((x * x) + 1.0);
}
↓
double code(double x) {
	return fma(x, x, 1.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot x + 1\]

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x, 1\right)\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  :precision binary64
  (+ (* x x) 1))