Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(-1 + x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{e}^{\left(-1 + x \cdot x\right)}
double f(double x) {
        double r1314470 = 1.0;
        double r1314471 = x;
        double r1314472 = r1314471 * r1314471;
        double r1314473 = r1314470 - r1314472;
        double r1314474 = -r1314473;
        double r1314475 = exp(r1314474);
        return r1314475;
}
↓
double f(double x) {
        double r1314476 = exp(1.0);
        double r1314477 = -1.0;
        double r1314478 = x;
        double r1314479 = r1314478 * r1314478;
        double r1314480 = r1314477 + r1314479;
        double r1314481 = pow(r1314476, r1314480);
        return r1314481;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{-1 + x \cdot x}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto e^{\color{blue}{1 \cdot \left(-1 + x \cdot x\right)}}\]

  5. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(-1 + x \cdot x\right)}}\]

  6. Simplified0.0

    \[\leadsto {\color{blue}{e}}^{\left(-1 + x \cdot x\right)}\]

  7. Final simplification0.0

    \[\leadsto {e}^{\left(-1 + x \cdot x\right)}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))