Average Error: 0.0 → 0.0
Time: 15.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{e^{x \cdot x}}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{e^{x \cdot x}}{e}
double f(double x) {
        double r1696730 = 1.0;
        double r1696731 = x;
        double r1696732 = r1696731 * r1696731;
        double r1696733 = r1696730 - r1696732;
        double r1696734 = -r1696733;
        double r1696735 = exp(r1696734);
        return r1696735;
}
↓
double f(double x) {
        double r1696736 = x;
        double r1696737 = r1696736 * r1696736;
        double r1696738 = exp(r1696737);
        double r1696739 = exp(1.0);
        double r1696740 = r1696738 / r1696739;
        return r1696740;
}

Error

Bits error versus x

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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. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{e^{{x}^{2} - 1}}\]

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto \frac{e^{x \cdot x}}{e}\]

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))