Average Error: 0.0 → 0.0
Time: 17.2s
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 r53385 = 1.0;
        double r53386 = x;
        double r53387 = r53386 * r53386;
        double r53388 = r53385 - r53387;
        double r53389 = -r53388;
        double r53390 = exp(r53389);
        return r53390;
}
↓
double f(double x) {
        double r53391 = x;
        double r53392 = 2.0;
        double r53393 = pow(r53391, r53392);
        double r53394 = 1.0;
        double r53395 = r53393 - r53394;
        double r53396 = exp(r53395);
        double r53397 = sqrt(r53396);
        double r53398 = r53397 * r53397;
        return r53398;
}

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)))))