Average Error: 0.0 → 0.0
Time: 7.6s
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 r694519 = 1.0;
        double r694520 = x;
        double r694521 = r694520 * r694520;
        double r694522 = r694519 - r694521;
        double r694523 = -r694522;
        double r694524 = exp(r694523);
        return r694524;
}
↓
double f(double x) {
        double r694525 = x;
        double r694526 = r694525 * r694525;
        double r694527 = exp(r694526);
        double r694528 = exp(1.0);
        double r694529 = r694527 / r694528;
        return r694529;
}

Error

Bits error versus x

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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 exp-sum0.0

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

  5. Simplified0.0

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

  6. Taylor expanded around inf 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))