Average Error: 0.0 → 0.0
Time: 18.0s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}
double f(double x) {
        double r29548 = 1.0;
        double r29549 = x;
        double r29550 = r29549 * r29549;
        double r29551 = r29548 - r29550;
        double r29552 = -r29551;
        double r29553 = exp(r29552);
        return r29553;
}
↓
double f(double x) {
        double r29554 = -1.0;
        double r29555 = exp(r29554);
        double r29556 = 1.0;
        double r29557 = x;
        double r29558 = r29557 * r29557;
        double r29559 = r29556 - r29558;
        double r29560 = pow(r29555, r29559);
        return r29560;
}

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 neg-mul-10.0

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

  4. Applied exp-prod0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))