Average Error: 0.0 → 0.0
Time: 1.2min
Precision: binary64
Cost: 320
\[x \cdot x + 1\]
↓
\[1 + x \cdot x\]
x \cdot x + 1
↓
1 + x \cdot x
(FPCore (x) :precision binary64 (+ (* x x) 1.0))
↓
(FPCore (x) :precision binary64 (+ 1.0 (* x x)))
double code(double x) {
	return (x * x) + 1.0;
}
↓
double code(double x) {
	return 1.0 + (x * x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error1.0
Cost641
\[\begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.751933474460368 \cdot 10^{-05}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}\]
Alternative 2
Error20.6
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 0.0

    \[x \cdot x + 1\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + x \cdot x}\]

  3. Final simplification0.0

    \[\leadsto 1 + x \cdot x\]

Reproduce

herbie shell --seed 2021040 
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  :precision binary64
  (+ (* x x) 1.0))