Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{\mathsf{fma}\left(x, x, -1\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{\mathsf{fma}\left(x, x, -1\right)}
double f(double x) {
        double r1571782 = 1.0;
        double r1571783 = x;
        double r1571784 = r1571783 * r1571783;
        double r1571785 = r1571782 - r1571784;
        double r1571786 = -r1571785;
        double r1571787 = exp(r1571786);
        return r1571787;
}
↓
double f(double x) {
        double r1571788 = x;
        double r1571789 = -1.0;
        double r1571790 = fma(r1571788, r1571788, r1571789);
        double r1571791 = exp(r1571790);
        return r1571791;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(x, x, -1\right)}}\]

  3. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(x, x, -1\right)}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))