Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
Cost: 6784
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(x \cdot x - 1\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{e}^{\left(x \cdot x - 1\right)}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (pow E (- (* x x) 1.0)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(((double) M_E), ((x * x) - 1.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.0
Cost6720
\[\frac{e^{x \cdot x}}{e}\]
Alternative 2
Error0.0
Cost6720
\[e^{x \cdot x - 1}\]
Alternative 3
Error0.7
Cost448
\[\frac{x \cdot x + 1}{e}\]
Alternative 4
Error52.6
Cost64
\[1\]

Error

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 *-un-lft-identity_binary64_780.0

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

  5. Applied exp-prod_binary64_1300.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))