Average Error: 49.1 → 0
Time: 2.6s
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 r955209 = 1.7e+308;
        double r955210 = t;
        double r955211 = r955209 * r955210;
        double r955212 = r955211 - r955209;
        return r955212;
}
↓
double f(double t) {
        double r955213 = 1.7e+308;
        double r955214 = t;
        double r955215 = -r955213;
        double r955216 = fma(r955213, r955214, r955215);
        return r955216;
}

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 2019152 +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))