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

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Results

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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 sub-neg_binary64_4120.0

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

  5. Applied exp-sum_binary64_4650.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020295 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))