Average Error: 0.0 → 0.0
Time: 10.2s
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 r1363292 = 1.0;
        double r1363293 = x;
        double r1363294 = r1363293 * r1363293;
        double r1363295 = r1363292 - r1363294;
        double r1363296 = -r1363295;
        double r1363297 = exp(r1363296);
        return r1363297;
}
↓
double f(double x) {
        double r1363298 = x;
        double r1363299 = r1363298 * r1363298;
        double r1363300 = 1.0;
        double r1363301 = r1363299 - r1363300;
        double r1363302 = exp(r1363301);
        return r1363302;
}

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 2019171 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))