Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)} \]
↓
\[{\left(e^{x}\right)}^{x} \cdot e^{-1} \]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x}\right)}^{x} \cdot e^{-1}

(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (* (pow (exp x) x) (exp -1.0)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(exp(x), x) * exp(-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

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

  3. Applied fma-udef_binary640.0

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

  4. Applied exp-sum_binary640.0

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

  5. Applied add-log-exp_binary640.0

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

  6. Applied exp-to-pow_binary640.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2022082 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))