Average Error: 0.0 → 0.0
Time: 13.9s
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 r1515684 = 1.0;
        double r1515685 = x;
        double r1515686 = r1515685 * r1515685;
        double r1515687 = r1515684 - r1515686;
        double r1515688 = -r1515687;
        double r1515689 = exp(r1515688);
        return r1515689;
}
↓
double f(double x) {
        double r1515690 = x;
        double r1515691 = r1515690 * r1515690;
        double r1515692 = 1.0;
        double r1515693 = r1515691 - r1515692;
        double r1515694 = exp(r1515693);
        return r1515694;
}

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 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))