Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{\frac{e^{1}}{e^{x \cdot x}}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{\frac{e^{1}}{e^{x \cdot x}}}
double f(double x) {
        double r21519 = 1.0;
        double r21520 = x;
        double r21521 = r21520 * r21520;
        double r21522 = r21519 - r21521;
        double r21523 = -r21522;
        double r21524 = exp(r21523);
        return r21524;
}
↓
double f(double x) {
        double r21525 = 1.0;
        double r21526 = 1.0;
        double r21527 = exp(r21526);
        double r21528 = x;
        double r21529 = r21528 * r21528;
        double r21530 = exp(r21529);
        double r21531 = r21527 / r21530;
        double r21532 = r21525 / r21531;
        return r21532;
}

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 add-log-exp0.0

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

  4. Applied add-log-exp0.0

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

  5. Applied diff-log0.0

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

  6. Applied neg-log0.0

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

  7. Applied rem-exp-log0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))