Average Error: 0.0 → 0.0
Time: 13.4s
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 r1210920 = 1.0;
        double r1210921 = x;
        double r1210922 = r1210921 * r1210921;
        double r1210923 = r1210920 - r1210922;
        double r1210924 = -r1210923;
        double r1210925 = exp(r1210924);
        return r1210925;
}
↓
double f(double x) {
        double r1210926 = x;
        double r1210927 = r1210926 * r1210926;
        double r1210928 = 1.0;
        double r1210929 = r1210927 - r1210928;
        double r1210930 = exp(r1210929);
        return r1210930;
}

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 2019158 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))