Average Error: 0.0 → 0.0
Time: 1.3s
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 r28530 = 1.0;
        double r28531 = x;
        double r28532 = r28531 * r28531;
        double r28533 = r28530 - r28532;
        double r28534 = -r28533;
        double r28535 = exp(r28534);
        return r28535;
}
↓
double f(double x) {
        double r28536 = 1.0;
        double r28537 = 1.0;
        double r28538 = x;
        double r28539 = r28538 * r28538;
        double r28540 = r28537 - r28539;
        double r28541 = exp(r28540);
        double r28542 = r28536 / r28541;
        return r28542;
}

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