Average Error: 0.0 → 0.0
Time: 8.7s
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 r1535018 = 1.0;
        double r1535019 = x;
        double r1535020 = r1535019 * r1535019;
        double r1535021 = r1535018 - r1535020;
        double r1535022 = -r1535021;
        double r1535023 = exp(r1535022);
        return r1535023;
}
↓
double f(double x) {
        double r1535024 = x;
        double r1535025 = r1535024 * r1535024;
        double r1535026 = 1.0;
        double r1535027 = r1535025 - r1535026;
        double r1535028 = exp(r1535027);
        return r1535028;
}

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 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))