Average Error: 0.0 → 0.0
Time: 9.5s
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 r1690895 = 1.0;
        double r1690896 = x;
        double r1690897 = r1690896 * r1690896;
        double r1690898 = r1690895 - r1690897;
        double r1690899 = -r1690898;
        double r1690900 = exp(r1690899);
        return r1690900;
}
↓
double f(double x) {
        double r1690901 = x;
        double r1690902 = r1690901 * r1690901;
        double r1690903 = 1.0;
        double r1690904 = r1690902 - r1690903;
        double r1690905 = exp(r1690904);
        return r1690905;
}

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 2019164 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))