Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{x \cdot x - 1}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x - 1}
double f(double x) {
        double r1380819 = 1.0;
        double r1380820 = x;
        double r1380821 = r1380820 * r1380820;
        double r1380822 = r1380819 - r1380821;
        double r1380823 = -r1380822;
        double r1380824 = exp(r1380823);
        return r1380824;
}
↓
double f(double x) {
        double r1380825 = x;
        double r1380826 = r1380825 * r1380825;
        double r1380827 = 1.0;
        double r1380828 = r1380826 - r1380827;
        double r1380829 = exp(r1380828);
        return r1380829;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))