Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{e}^{\left(x \cdot x\right)}}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{e}^{\left(x \cdot x\right)}}{e}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (/ (pow E (* x x)) E))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(((double) M_E), (x * x)) / ((double) M_E);
}

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 *-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. Using strategy rm

  8. Applied pow-sub_binary64_1540.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2021024 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))