Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{\sqrt{1} + x}\right)}^{\left(-\left(\sqrt{1} - x\right)\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{\sqrt{1} + x}\right)}^{\left(-\left(\sqrt{1} - x\right)\right)}
double f(double x) {
        double r36452 = 1.0;
        double r36453 = x;
        double r36454 = r36453 * r36453;
        double r36455 = r36452 - r36454;
        double r36456 = -r36455;
        double r36457 = exp(r36456);
        return r36457;
}
↓
double f(double x) {
        double r36458 = 1.0;
        double r36459 = sqrt(r36458);
        double r36460 = x;
        double r36461 = r36459 + r36460;
        double r36462 = exp(r36461);
        double r36463 = r36459 - r36460;
        double r36464 = -r36463;
        double r36465 = pow(r36462, r36464);
        return r36465;
}

Error

Bits error versus x

Try it out

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied difference-of-squares0.0

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

  5. Applied distribute-rgt-neg-in0.0

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

  6. Applied exp-prod0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019318 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))