Average Error: 0.0 → 0.0
Time: 8.8s
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 r1546241 = 1.0;
        double r1546242 = x;
        double r1546243 = r1546242 * r1546242;
        double r1546244 = r1546241 - r1546243;
        double r1546245 = -r1546244;
        double r1546246 = exp(r1546245);
        return r1546246;
}
↓
double f(double x) {
        double r1546247 = x;
        double r1546248 = r1546247 * r1546247;
        double r1546249 = 1.0;
        double r1546250 = r1546248 - r1546249;
        double r1546251 = exp(r1546250);
        return r1546251;
}

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 2019172 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))