Average Error: 49.1 → 0
Time: 4.9s
Precision: 64
\[1.9 \le t \le 2.1\]
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
↓
\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)\]
1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}
↓
\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)
double f(double t) {
        double r1806723 = 1.7e+308;
        double r1806724 = t;
        double r1806725 = r1806723 * r1806724;
        double r1806726 = r1806725 - r1806723;
        return r1806726;
}
↓
double f(double t) {
        double r1806727 = 1.7e+308;
        double r1806728 = t;
        double r1806729 = -r1806727;
        double r1806730 = fma(r1806727, r1806728, r1806729);
        return r1806730;
}

Error

Bits error versus t

Target

Original49.1
Target0
Herbie0
\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)\]

Derivation

  1. Initial program 49.1

    \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (t)
  :name "fma_test2"
  :pre (<= 1.9 t 2.1)

  :herbie-target
  (fma 1.7e+308 t (- 1.7e+308))

  (- (* 1.7e+308 t) 1.7e+308))