Average Error: 0.0 → 0.0
Time: 8.0s
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 r1032170 = 1.0;
        double r1032171 = x;
        double r1032172 = r1032171 * r1032171;
        double r1032173 = r1032170 - r1032172;
        double r1032174 = -r1032173;
        double r1032175 = exp(r1032174);
        return r1032175;
}
↓
double f(double x) {
        double r1032176 = x;
        double r1032177 = r1032176 * r1032176;
        double r1032178 = 1.0;
        double r1032179 = r1032177 - r1032178;
        double r1032180 = exp(r1032179);
        return r1032180;
}

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)))))