Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{x \cdot x - 1}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x - 1}
double f(double x) {
        double r41639 = 1.0;
        double r41640 = x;
        double r41641 = r41640 * r41640;
        double r41642 = r41639 - r41641;
        double r41643 = -r41642;
        double r41644 = exp(r41643);
        return r41644;
}
↓
double f(double x) {
        double r41645 = x;
        double r41646 = r41645 * r41645;
        double r41647 = 1.0;
        double r41648 = r41646 - r41647;
        double r41649 = exp(r41648);
        return r41649;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))