Average Error: 0.0 → 0.0
Time: 11.0s
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 r1374601 = 1.0;
        double r1374602 = x;
        double r1374603 = r1374602 * r1374602;
        double r1374604 = r1374601 - r1374603;
        double r1374605 = -r1374604;
        double r1374606 = exp(r1374605);
        return r1374606;
}
↓
double f(double x) {
        double r1374607 = x;
        double r1374608 = -1.0;
        double r1374609 = fma(r1374607, r1374607, r1374608);
        double r1374610 = exp(r1374609);
        return r1374610;
}

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 2019104 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))