Average Error: 0.0 → 0.0
Time: 1.8s
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 r30670 = 1.0;
        double r30671 = x;
        double r30672 = r30671 * r30671;
        double r30673 = r30670 - r30672;
        double r30674 = -r30673;
        double r30675 = exp(r30674);
        return r30675;
}
↓
double f(double x) {
        double r30676 = 1.0;
        double r30677 = sqrt(r30676);
        double r30678 = x;
        double r30679 = r30677 + r30678;
        double r30680 = exp(r30679);
        double r30681 = r30677 - r30678;
        double r30682 = -r30681;
        double r30683 = pow(r30680, r30682);
        return r30683;
}

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 2020056 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))