Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-\left(1 - x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-\left(1 - x \cdot x\right)}
double f(double x) {
        double r18111 = 1.0;
        double r18112 = x;
        double r18113 = r18112 * r18112;
        double r18114 = r18111 - r18113;
        double r18115 = -r18114;
        double r18116 = exp(r18115);
        return r18116;
}
↓
double f(double x) {
        double r18117 = 1.0;
        double r18118 = x;
        double r18119 = r18118 * r18118;
        double r18120 = r18117 - r18119;
        double r18121 = -r18120;
        double r18122 = exp(r18121);
        return r18122;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))