Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\left(\sqrt{\frac{1}{e}} \cdot e^{x \cdot x}\right) \cdot \sqrt{\frac{1}{e}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\left(\sqrt{\frac{1}{e}} \cdot e^{x \cdot x}\right) \cdot \sqrt{\frac{1}{e}}
double f(double x) {
        double r1561428 = 1.0;
        double r1561429 = x;
        double r1561430 = r1561429 * r1561429;
        double r1561431 = r1561428 - r1561430;
        double r1561432 = -r1561431;
        double r1561433 = exp(r1561432);
        return r1561433;
}
↓
double f(double x) {
        double r1561434 = 1.0;
        double r1561435 = exp(1.0);
        double r1561436 = r1561434 / r1561435;
        double r1561437 = sqrt(r1561436);
        double r1561438 = x;
        double r1561439 = r1561438 * r1561438;
        double r1561440 = exp(r1561439);
        double r1561441 = r1561437 * r1561440;
        double r1561442 = r1561441 * r1561437;
        return r1561442;
}

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

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(x, x, -1\right)}}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

    \[\leadsto e^{x \cdot x} \cdot \color{blue}{\frac{1}{e}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.0

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

  9. Applied associate-*r*0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))