Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)} \cdot {\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)} \cdot {\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)}
double f(double x) {
        double r38121 = 1.0;
        double r38122 = x;
        double r38123 = r38122 * r38122;
        double r38124 = r38121 - r38123;
        double r38125 = -r38124;
        double r38126 = exp(r38125);
        return r38126;
}
↓
double f(double x) {
        double r38127 = 1.0;
        double r38128 = sqrt(r38127);
        double r38129 = x;
        double r38130 = r38128 + r38129;
        double r38131 = exp(r38130);
        double r38132 = r38128 - r38129;
        double r38133 = -r38132;
        double r38134 = 2.0;
        double r38135 = r38133 / r38134;
        double r38136 = pow(r38131, r38135);
        double r38137 = r38136 * r38136;
        return r38137;
}

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 sqr-pow0.0

    \[\leadsto \color{blue}{{\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)} \cdot {\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)}}\]

  9. Final simplification0.0

    \[\leadsto {\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)} \cdot {\left(e^{\sqrt{1} + x}\right)}^{\left(\frac{-\left(\sqrt{1} - x\right)}{2}\right)}\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))