Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (pow (exp (+ x (sqrt 1.0))) (- x (sqrt 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(((double) (x + ((double) sqrt(1.0)))))), ((double) (x - ((double) sqrt(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 add-sqr-sqrtError: 0.0 bits

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

  5. Applied difference-of-squaresError: 0.0 bits

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

  6. Applied exp-prodError: 0.0 bits

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

  7. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020205 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))