Average Error: 64.0 → 0
Time: 4.2s
Precision: 64
\[1.899999999999999911182158029987476766109 \le t \le 2.100000000000000088817841970012523233891\]
\[1.699999999999999938830795788659981743333 \cdot 10^{308} \cdot t - 1.699999999999999938830795788659981743333 \cdot 10^{308}\]
↓
\[\mathsf{fma}\left(1.699999999999999938830795788659981743333 \cdot 10^{308}, t, -1.699999999999999938830795788659981743333 \cdot 10^{308}\right)\]
1.699999999999999938830795788659981743333 \cdot 10^{308} \cdot t - 1.699999999999999938830795788659981743333 \cdot 10^{308}
↓
\mathsf{fma}\left(1.699999999999999938830795788659981743333 \cdot 10^{308}, t, -1.699999999999999938830795788659981743333 \cdot 10^{308}\right)
double f(double t) {
        double r44436 = 1.7e+308;
        double r44437 = t;
        double r44438 = r44436 * r44437;
        double r44439 = r44438 - r44436;
        return r44439;
}
↓
double f(double t) {
        double r44440 = 1.7e+308;
        double r44441 = t;
        double r44442 = -r44440;
        double r44443 = fma(r44440, r44441, r44442);
        return r44443;
}

Error

Bits error versus t

Target

Original64.0
Target0
Herbie0
\[\mathsf{fma}\left(1.699999999999999938830795788659981743333 \cdot 10^{308}, t, -1.699999999999999938830795788659981743333 \cdot 10^{308}\right)\]

Derivation

  1. Initial program 64.0

    \[1.699999999999999938830795788659981743333 \cdot 10^{308} \cdot t - 1.699999999999999938830795788659981743333 \cdot 10^{308}\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.699999999999999938830795788659981743333 \cdot 10^{308}, t, -1.699999999999999938830795788659981743333 \cdot 10^{308}\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(1.699999999999999938830795788659981743333 \cdot 10^{308}, t, -1.699999999999999938830795788659981743333 \cdot 10^{308}\right)\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (<= 1.8999999999999999 t 2.10000000000000009)

  :herbie-target
  (fma 1.6999999999999999e308 t (- 1.6999999999999999e308))

  (- (* 1.6999999999999999e308 t) 1.6999999999999999e308))