Average Error: 0.0 → 0.0
Time: 12.3s
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 r1223542 = 1.0;
        double r1223543 = x;
        double r1223544 = r1223543 * r1223543;
        double r1223545 = r1223542 - r1223544;
        double r1223546 = -r1223545;
        double r1223547 = exp(r1223546);
        return r1223547;
}
↓
double f(double x) {
        double r1223548 = x;
        double r1223549 = -1.0;
        double r1223550 = fma(r1223548, r1223548, r1223549);
        double r1223551 = exp(r1223550);
        return r1223551;
}

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 2019112 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))