Average Error: 0.0 → 0.0
Time: 10.0s
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 r1380821 = 1.0;
        double r1380822 = x;
        double r1380823 = r1380822 * r1380822;
        double r1380824 = r1380821 - r1380823;
        double r1380825 = -r1380824;
        double r1380826 = exp(r1380825);
        return r1380826;
}
↓
double f(double x) {
        double r1380827 = x;
        double r1380828 = r1380827 * r1380827;
        double r1380829 = 1.0;
        double r1380830 = r1380828 - r1380829;
        double r1380831 = exp(r1380830);
        return r1380831;
}

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)))))