Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{\frac{{\left(e^{x}\right)}^{x}}{\sqrt{e}}}{\sqrt{e}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{\frac{{\left(e^{x}\right)}^{x}}{\sqrt{e}}}{\sqrt{e}}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (/ (/ (pow (exp x) x) (sqrt E)) (sqrt E)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return (pow(exp(x), x) / sqrt((double) M_E)) / sqrt((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 exp-diff_binary640.0

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

  5. Simplified0.0

    \[\leadsto \frac{e^{x \cdot x}}{\color{blue}{e}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt_binary641.0

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

  8. Applied associate-/r*_binary640.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020219 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))