Average Error: 0.0 → 0.0
Time: 10.8s
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 r1858043 = 1.0;
        double r1858044 = x;
        double r1858045 = r1858044 * r1858044;
        double r1858046 = r1858043 - r1858045;
        double r1858047 = -r1858046;
        double r1858048 = exp(r1858047);
        return r1858048;
}
↓
double f(double x) {
        double r1858049 = x;
        double r1858050 = r1858049 * r1858049;
        double r1858051 = 1.0;
        double r1858052 = r1858050 - r1858051;
        double r1858053 = exp(r1858052);
        return r1858053;
}

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 2019174 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))