Average Error: 0.0 → 0.0
Time: 9.7s
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 r1415438 = 1.0;
        double r1415439 = x;
        double r1415440 = r1415439 * r1415439;
        double r1415441 = r1415438 - r1415440;
        double r1415442 = -r1415441;
        double r1415443 = exp(r1415442);
        return r1415443;
}
↓
double f(double x) {
        double r1415444 = x;
        double r1415445 = r1415444 * r1415444;
        double r1415446 = 1.0;
        double r1415447 = r1415445 - r1415446;
        double r1415448 = exp(r1415447);
        return r1415448;
}

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 2019170 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))