Average Error: 0.0 → 0.0
Time: 3.6s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)} \]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{x}\right)}^{x}\right)\right) \cdot e^{-1} \]
e^{-\left(1 - x \cdot x\right)}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{x}\right)}^{x}\right)\right) \cdot e^{-1}

(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (* (expm1 (log1p (pow (exp x) x))) (exp -1.0)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return expm1(log1p(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 egg-rr0.0

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

  4. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{x}\right)}^{x}\right)\right)} \cdot e^{-1} \]

  5. Final simplification0.0

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{x}\right)}^{x}\right)\right) \cdot e^{-1} \]

Reproduce

herbie shell --seed 2022127 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))