Average Error: 0.0 → 0.0
Time: 13.7s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{{x}^{2} + \left(-1\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{{x}^{2} + \left(-1\right)}
double f(double x) {
        double r23634 = 1.0;
        double r23635 = x;
        double r23636 = r23635 * r23635;
        double r23637 = r23634 - r23636;
        double r23638 = -r23637;
        double r23639 = exp(r23638);
        return r23639;
}
↓
double f(double x) {
        double r23640 = x;
        double r23641 = 2.0;
        double r23642 = pow(r23640, r23641);
        double r23643 = 1.0;
        double r23644 = -r23643;
        double r23645 = r23642 + r23644;
        double r23646 = exp(r23645);
        return r23646;
}

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 sub-neg0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))