Average Error: 0.0 → 0.0
Time: 3.3s
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 r519051 = 1.0;
        double r519052 = x;
        double r519053 = r519052 * r519052;
        double r519054 = r519051 - r519053;
        double r519055 = -r519054;
        double r519056 = exp(r519055);
        return r519056;
}
↓
double f(double x) {
        double r519057 = x;
        double r519058 = r519057 * r519057;
        double r519059 = -1.0;
        double r519060 = r519058 + r519059;
        double r519061 = exp(r519060);
        return r519061;
}

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 2019152 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))