Average Error: 0.0 → 0.0
Time: 11.3s
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 r41476 = 1.0;
        double r41477 = x;
        double r41478 = r41477 * r41477;
        double r41479 = r41476 - r41478;
        double r41480 = -r41479;
        double r41481 = exp(r41480);
        return r41481;
}
↓
double f(double x) {
        double r41482 = x;
        double r41483 = 2.0;
        double r41484 = pow(r41482, r41483);
        double r41485 = 1.0;
        double r41486 = r41484 - r41485;
        double r41487 = exp(r41486);
        double r41488 = sqrt(r41487);
        double r41489 = r41488 * r41488;
        return r41489;
}

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