Average Error: 0.0 → 0.0
Time: 7.7s
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 r1391580 = 1.0;
        double r1391581 = x;
        double r1391582 = r1391581 * r1391581;
        double r1391583 = r1391580 - r1391582;
        double r1391584 = -r1391583;
        double r1391585 = exp(r1391584);
        return r1391585;
}
↓
double f(double x) {
        double r1391586 = x;
        double r1391587 = r1391586 * r1391586;
        double r1391588 = -1.0;
        double r1391589 = r1391587 + r1391588;
        double r1391590 = exp(r1391589);
        return r1391590;
}

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 2019165 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))