Average Error: 0.0 → 0.0
Time: 16.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{e^{x \cdot x}}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{e^{x \cdot x}}{e}
double f(double x) {
        double r1509945 = 1.0;
        double r1509946 = x;
        double r1509947 = r1509946 * r1509946;
        double r1509948 = r1509945 - r1509947;
        double r1509949 = -r1509948;
        double r1509950 = exp(r1509949);
        return r1509950;
}
↓
double f(double x) {
        double r1509951 = x;
        double r1509952 = r1509951 * r1509951;
        double r1509953 = exp(r1509952);
        double r1509954 = exp(1.0);
        double r1509955 = r1509953 / r1509954;
        return r1509955;
}

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. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{e^{{x}^{2} - 1}}\]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))