Average Error: 64.0 → 0
Time: 4.4s
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 r9422 = 1.7e+308;
        double r9423 = t;
        double r9424 = r9422 * r9423;
        double r9425 = r9424 - r9422;
        return r9425;
}
↓
double f(double t) {
        double r9426 = 1.7e+308;
        double r9427 = t;
        double r9428 = -r9426;
        double r9429 = fma(r9426, r9427, r9428);
        return r9429;
}

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 2019315 +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))