Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(x \cdot x - 1\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{e}^{\left(x \cdot x - 1\right)}
double f(double x) {
        double r27029 = 1.0;
        double r27030 = x;
        double r27031 = r27030 * r27030;
        double r27032 = r27029 - r27031;
        double r27033 = -r27032;
        double r27034 = exp(r27033);
        return r27034;
}
↓
double f(double x) {
        double r27035 = exp(1.0);
        double r27036 = x;
        double r27037 = r27036 * r27036;
        double r27038 = 1.0;
        double r27039 = r27037 - r27038;
        double r27040 = pow(r27035, r27039);
        return r27040;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

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

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

  5. Applied exp-prod0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))