Average Error: 0.0 → 0.0
Time: 10.3s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt{e^{{x}^{2} - 1}} \cdot \sqrt{e^{{x}^{2} - 1}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\sqrt{e^{{x}^{2} - 1}} \cdot \sqrt{e^{{x}^{2} - 1}}
double f(double x) {
        double r42263 = 1.0;
        double r42264 = x;
        double r42265 = r42264 * r42264;
        double r42266 = r42263 - r42265;
        double r42267 = -r42266;
        double r42268 = exp(r42267);
        return r42268;
}
↓
double f(double x) {
        double r42269 = x;
        double r42270 = 2.0;
        double r42271 = pow(r42269, r42270);
        double r42272 = 1.0;
        double r42273 = r42271 - r42272;
        double r42274 = exp(r42273);
        double r42275 = sqrt(r42274);
        double r42276 = r42275 * r42275;
        return r42276;
}

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

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

  4. Simplified0.0

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

  5. Simplified0.0

    \[\leadsto \sqrt{e^{{x}^{2} - 1}} \cdot \color{blue}{\sqrt{e^{{x}^{2} - 1}}}\]

  6. Final simplification0.0

    \[\leadsto \sqrt{e^{{x}^{2} - 1}} \cdot \sqrt{e^{{x}^{2} - 1}}\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))