Average Error: 49.2 → 0
Time: 1.9s
Precision: 64
\[1.9 \le t \le 2.1\]
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
↓
\[(\left( 1.7 \cdot 10^{+308} \right) \cdot t + \left(-1.7 \cdot 10^{+308}\right))_*\]
1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}
↓
(\left( 1.7 \cdot 10^{+308} \right) \cdot t + \left(-1.7 \cdot 10^{+308}\right))_*
double f(double t) {
        double r1914879 = 1.7e+308;
        double r1914880 = t;
        double r1914881 = r1914879 * r1914880;
        double r1914882 = r1914881 - r1914879;
        return r1914882;
}
↓
double f(double t) {
        double r1914883 = 1.7e+308;
        double r1914884 = t;
        double r1914885 = -r1914883;
        double r1914886 = fma(r1914883, r1914884, r1914885);
        return r1914886;
}

Error

Bits error versus t

Target

Original49.2
Target0
Herbie0
\[(\left( 1.7 \cdot 10^{+308} \right) \cdot t + \left(-1.7 \cdot 10^{+308}\right))_*\]

Derivation

  1. Initial program 49.2

    \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
  2. Using strategy rm

  3. Applied fma-neg0

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

  4. Final simplification0

    \[\leadsto (\left( 1.7 \cdot 10^{+308} \right) \cdot t + \left(-1.7 \cdot 10^{+308}\right))_*\]

Reproduce

herbie shell --seed 2019104 +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))