Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt{{\left(e^{\sqrt{1} + x}\right)}^{\left(-\left(\sqrt{1} - x\right)\right)}} \cdot \sqrt{{\left(e^{\sqrt{1} + x}\right)}^{\left(-\left(\sqrt{1} - x\right)\right)}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\sqrt{{\left(e^{\sqrt{1} + x}\right)}^{\left(-\left(\sqrt{1} - x\right)\right)}} \cdot \sqrt{{\left(e^{\sqrt{1} + x}\right)}^{\left(-\left(\sqrt{1} - x\right)\right)}}
double f(double x) {
        double r29285 = 1.0;
        double r29286 = x;
        double r29287 = r29286 * r29286;
        double r29288 = r29285 - r29287;
        double r29289 = -r29288;
        double r29290 = exp(r29289);
        return r29290;
}
↓
double f(double x) {
        double r29291 = 1.0;
        double r29292 = sqrt(r29291);
        double r29293 = x;
        double r29294 = r29292 + r29293;
        double r29295 = exp(r29294);
        double r29296 = r29292 - r29293;
        double r29297 = -r29296;
        double r29298 = pow(r29295, r29297);
        double r29299 = sqrt(r29298);
        double r29300 = r29299 * r29299;
        return r29300;
}

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. Using strategy rm

  8. Applied add-sqr-sqrt0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))