Average Error: 0.0 → 0.0
Time: 3.4s
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 r561663 = 1.0;
        double r561664 = x;
        double r561665 = r561664 * r561664;
        double r561666 = r561663 - r561665;
        double r561667 = -r561666;
        double r561668 = exp(r561667);
        return r561668;
}
↓
double f(double x) {
        double r561669 = x;
        double r561670 = r561669 * r561669;
        double r561671 = -1.0;
        double r561672 = r561670 + r561671;
        double r561673 = exp(r561672);
        return r561673;
}

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 2019154 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))