Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{-1 - x}\right)}^{\left(1 - x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{-1 - x}\right)}^{\left(1 - x\right)}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (pow (exp (- -1.0 x)) (- 1.0 x)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(exp(-1.0 - x), (1.0 - x));
}

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

    \[e^{-\left(1 - x \cdot x\right)}\]
  2. Using strategy rm

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

    \[\leadsto e^{-\left(\color{blue}{1 \cdot 1} - x \cdot x\right)}\]

  4. Applied difference-of-squares_binary640.0

    \[\leadsto e^{-\color{blue}{\left(1 + x\right) \cdot \left(1 - x\right)}}\]

  5. Applied distribute-lft-neg-in_binary640.0

    \[\leadsto e^{\color{blue}{\left(-\left(1 + x\right)\right) \cdot \left(1 - x\right)}}\]

  6. Applied exp-prod_binary640.0

    \[\leadsto \color{blue}{{\left(e^{-\left(1 + x\right)}\right)}^{\left(1 - x\right)}}\]

  7. Simplified0.0

    \[\leadsto {\color{blue}{\left(e^{-1 - x}\right)}}^{\left(1 - x\right)}\]

  8. Final simplification0.0

    \[\leadsto {\left(e^{-1 - x}\right)}^{\left(1 - x\right)}\]

Reproduce

herbie shell --seed 2020273 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))