Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x}\right)}^{\left(x + -1\right)} \cdot e^{x + -1}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x}\right)}^{\left(x + -1\right)} \cdot e^{x + -1}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (* (pow (exp x) (+ x -1.0)) (exp (+ x -1.0))))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(exp(x), (x + -1.0)) * exp(x + -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 difference-of-sqr-1_binary64_3890.0

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

  5. Applied exp-prod_binary64_4710.0

    \[\leadsto \color{blue}{{\left(e^{x + 1}\right)}^{\left(x - 1\right)}}\]
  6. Using strategy rm

  7. Applied exp-sum_binary64_4650.0

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

  8. Applied unpow-prod-down_binary64_4980.0

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

  9. Simplified0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2021023 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))