Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{{x}^{2}}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot e^{{x}^{2}}
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return (exp(-1.0) * exp(pow(x, 2.0)));
}

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

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

  3. Applied sub-neg0.0

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

  4. Applied distribute-neg-in0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

    \[\leadsto e^{-1} \cdot \color{blue}{e^{{x}^{2}}}\]

  7. Final simplification0.0

    \[\leadsto e^{-1} \cdot e^{{x}^{2}}\]

Reproduce

herbie shell --seed 2020075 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))