Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot {\left(e^{x}\right)}^{x}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot {\left(e^{x}\right)}^{x}
double f(double x) {
        double r37498 = 1.0;
        double r37499 = x;
        double r37500 = r37499 * r37499;
        double r37501 = r37498 - r37500;
        double r37502 = -r37501;
        double r37503 = exp(r37502);
        return r37503;
}
↓
double f(double x) {
        double r37504 = 1.0;
        double r37505 = -r37504;
        double r37506 = exp(r37505);
        double r37507 = x;
        double r37508 = exp(r37507);
        double r37509 = pow(r37508, r37507);
        double r37510 = r37506 * r37509;
        return r37510;
}

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. Applied distribute-neg-in0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))