Average Error: 49.1 → 0
Time: 3.5s
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 r1388483 = 1.7e+308;
        double r1388484 = t;
        double r1388485 = r1388483 * r1388484;
        double r1388486 = r1388485 - r1388483;
        return r1388486;
}
↓
double f(double t) {
        double r1388487 = 1.7e+308;
        double r1388488 = t;
        double r1388489 = -r1388487;
        double r1388490 = fma(r1388487, r1388488, r1388489);
        return r1388490;
}

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 2019130 +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))