Average Error: 0.0 → 0.0
Time: 18.9s
Precision: 64
\[e^{-\left(1.0 - x \cdot x\right)}\]
↓
\[e^{x \cdot x - 1.0}\]
e^{-\left(1.0 - x \cdot x\right)}
↓
e^{x \cdot x - 1.0}
double f(double x) {
        double r1590493 = 1.0;
        double r1590494 = x;
        double r1590495 = r1590494 * r1590494;
        double r1590496 = r1590493 - r1590495;
        double r1590497 = -r1590496;
        double r1590498 = exp(r1590497);
        return r1590498;
}
↓
double f(double x) {
        double r1590499 = x;
        double r1590500 = r1590499 * r1590499;
        double r1590501 = 1.0;
        double r1590502 = r1590500 - r1590501;
        double r1590503 = exp(r1590502);
        return r1590503;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[e^{-\left(1.0 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1.0}}\]

  3. Final simplification0.0

    \[\leadsto e^{x \cdot x - 1.0}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))