Average Error: 0.0 → 0.0
Time: 898.0ms
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(x \cdot x - 1\right)}\]
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 ((double) exp(((double) -(((double) (1.0 - ((double) (x * x))))))));
}
↓
double code(double x) {
	return ((double) pow(((double) M_E), ((double) (((double) (x * x)) - 1.0))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.0 bits

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

  2. SimplifiedError: 0.0 bits

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

  4. Applied *-un-lft-identityError: 0.0 bits

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

  5. Applied exp-prodError: 0.0 bits

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

  6. SimplifiedError: 0.0 bits

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

  7. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))