Average Error: 49.1 → 0
Time: 1.6s
Precision: 64
\[1.9 \le t \le 2.1\]
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
↓
\[\mathsf{fma}\left(\left( 1.7 \cdot 10^{+308} \right), t, \left(-1.7 \cdot 10^{+308}\right)\right)\]
1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}
↓
\mathsf{fma}\left(\left( 1.7 \cdot 10^{+308} \right), t, \left(-1.7 \cdot 10^{+308}\right)\right)
double f(double t) {
        double r5163796 = 1.7e+308;
        double r5163797 = t;
        double r5163798 = r5163796 * r5163797;
        double r5163799 = r5163798 - r5163796;
        return r5163799;
}
↓
double f(double t) {
        double r5163800 = 1.7e+308;
        double r5163801 = t;
        double r5163802 = -r5163800;
        double r5163803 = fma(r5163800, r5163801, r5163802);
        return r5163803;
}

Error

Bits error versus t

Target

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

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

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019124 +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))