Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{\left(e^{x}\right)}^{x}}{e^{1}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{\left(e^{x}\right)}^{x}}{e^{1}}
double f(double x) {
        double r32369 = 1.0;
        double r32370 = x;
        double r32371 = r32370 * r32370;
        double r32372 = r32369 - r32371;
        double r32373 = -r32372;
        double r32374 = exp(r32373);
        return r32374;
}
↓
double f(double x) {
        double r32375 = x;
        double r32376 = exp(r32375);
        double r32377 = pow(r32376, r32375);
        double r32378 = 1.0;
        double r32379 = exp(r32378);
        double r32380 = r32377 / r32379;
        return r32380;
}

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. Using strategy rm

  4. Applied exp-diff0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))