Average Error: 49.1 → 0
Time: 1.5s
Precision: 64
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
↓
\[(\left( 1.7 \cdot 10^{+308} \right) \cdot t + \left(-1.7 \cdot 10^{+308}\right))_*\]
double f(double t) {
        double r7610021 = 1.7e+308;
        double r7610022 = t;
        double r7610023 = r7610021 * r7610022;
        double r7610024 = r7610023 - r7610021;
        return r7610024;
}
↓
double f(double t) {
        double r7610025 = 1.7e+308;
        double r7610026 = t;
        double r7610027 = -r7610025;
        double r7610028 = fma(r7610025, r7610026, r7610027);
        return r7610028;
}


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))_*

Error

Bits error versus t

Target

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

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

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019102 +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))