Average Error: 0.0 → 0.0
Time: 11.5s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{x \cdot x}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot e^{x \cdot x}
double f(double x) {
        double r15903 = 1.0;
        double r15904 = x;
        double r15905 = r15904 * r15904;
        double r15906 = r15903 - r15905;
        double r15907 = -r15906;
        double r15908 = exp(r15907);
        return r15908;
}
↓
double f(double x) {
        double r15909 = 1.0;
        double r15910 = -r15909;
        double r15911 = exp(r15910);
        double r15912 = x;
        double r15913 = r15912 * r15912;
        double r15914 = exp(r15913);
        double r15915 = r15911 * r15914;
        return r15915;
}

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))