Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{\left(e^{x}\right)}^{x}}{e^{1}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{\left(e^{x}\right)}^{x}}{e^{1}}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (/ (pow (exp x) x) (exp 1.0)))
double code(double x) {
	return ((double) exp(((double) -(((double) (1.0 - ((double) (x * x))))))));
}
↓
double code(double x) {
	return (((double) pow(((double) exp(x)), x)) / ((double) exp(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

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

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1}}\]
  3. Using strategy rm

  4. Applied exp-diff0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))