Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{e^{1 - x \cdot x}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{e^{1 - x \cdot x}}
double f(double x) {
        double r18531 = 1.0;
        double r18532 = x;
        double r18533 = r18532 * r18532;
        double r18534 = r18531 - r18533;
        double r18535 = -r18534;
        double r18536 = exp(r18535);
        return r18536;
}
↓
double f(double x) {
        double r18537 = 1.0;
        double r18538 = 1.0;
        double r18539 = x;
        double r18540 = r18539 * r18539;
        double r18541 = r18538 - r18540;
        double r18542 = exp(r18541);
        double r18543 = r18537 / r18542;
        return r18543;
}

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 exp-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))