Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)} \]
↓
\[e^{x \cdot x} \cdot e^{-1} \]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x} \cdot e^{-1}

(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (* (exp (* x x)) (exp -1.0)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return 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 *-un-lft-identity_binary640.0

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

  4. Applied exp-prod_binary640.0

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

  5. Simplified0.0

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

  6. Applied fma-udef_binary640.0

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

  7. Applied unpow-prod-up_binary640.0

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

  8. Simplified0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2021215 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))