Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{\frac{-1 + {x}^{6}}{{x}^{4} + \left(x \cdot x + 1\right)}}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{\frac{-1 + {x}^{6}}{{x}^{4} + \left(x \cdot x + 1\right)}}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x)
 :precision binary64
 (exp (/ (+ -1.0 (pow x 6.0)) (+ (pow x 4.0) (+ (* x x) 1.0)))))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return exp((-1.0 + pow(x, 6.0)) / (pow(x, 4.0) + ((x * 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 flip3--_binary64_4230.0

    \[\leadsto e^{\color{blue}{\frac{{\left(x \cdot x\right)}^{3} - {1}^{3}}{\left(x \cdot x\right) \cdot \left(x \cdot x\right) + \left(1 \cdot 1 + \left(x \cdot x\right) \cdot 1\right)}}}\]

  5. Simplified0.0

    \[\leadsto e^{\frac{\color{blue}{-1 + {x}^{6}}}{\left(x \cdot x\right) \cdot \left(x \cdot x\right) + \left(1 \cdot 1 + \left(x \cdot x\right) \cdot 1\right)}}\]

  6. Simplified0.0

    \[\leadsto e^{\frac{-1 + {x}^{6}}{\color{blue}{{x}^{4} + \left(x \cdot x + 1\right)}}}\]

  7. Final simplification0.0

    \[\leadsto e^{\frac{-1 + {x}^{6}}{{x}^{4} + \left(x \cdot x + 1\right)}}\]

Reproduce

herbie shell --seed 2021098 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))