Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{(x \cdot x + -1)_*}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{(x \cdot x + -1)_*}
double f(double x) {
        double r1294437 = 1.0;
        double r1294438 = x;
        double r1294439 = r1294438 * r1294438;
        double r1294440 = r1294437 - r1294439;
        double r1294441 = -r1294440;
        double r1294442 = exp(r1294441);
        return r1294442;
}
↓
double f(double x) {
        double r1294443 = x;
        double r1294444 = -1.0;
        double r1294445 = fma(r1294443, r1294443, r1294444);
        double r1294446 = exp(r1294445);
        return r1294446;
}

Error

Bits error versus x

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. Final simplification0.0

    \[\leadsto e^{(x \cdot x + -1)_*}\]

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))