Average Error: 0.0 → 0.0
Time: 2.8s
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 r27476 = 1.0;
        double r27477 = x;
        double r27478 = r27477 * r27477;
        double r27479 = r27476 - r27478;
        double r27480 = -r27479;
        double r27481 = exp(r27480);
        return r27481;
}
↓
double f(double x) {
        double r27482 = 1.0;
        double r27483 = sqrt(r27482);
        double r27484 = x;
        double r27485 = r27483 + r27484;
        double r27486 = exp(r27485);
        double r27487 = r27483 - r27484;
        double r27488 = -r27487;
        double r27489 = pow(r27486, r27488);
        double r27490 = sqrt(r27489);
        double r27491 = r27490 * r27490;
        return r27491;
}

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 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))