Average Error: 0.0 → 0.0
Time: 10.9s
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 r1484891 = 1.0;
        double r1484892 = x;
        double r1484893 = r1484892 * r1484892;
        double r1484894 = r1484891 - r1484893;
        double r1484895 = -r1484894;
        double r1484896 = exp(r1484895);
        return r1484896;
}
↓
double f(double x) {
        double r1484897 = x;
        double r1484898 = r1484897 * r1484897;
        double r1484899 = 1.0;
        double r1484900 = r1484898 - r1484899;
        double r1484901 = exp(r1484900);
        return r1484901;
}

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 2019171 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))