Average Error: 49.1 → 0
Time: 1.5s
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 r17935939 = 1.7e+308;
        double r17935940 = t;
        double r17935941 = r17935939 * r17935940;
        double r17935942 = r17935941 - r17935939;
        return r17935942;
}
↓
double f(double t) {
        double r17935943 = 1.7e+308;
        double r17935944 = t;
        double r17935945 = -r17935943;
        double r17935946 = fma(r17935943, r17935944, r17935945);
        return r17935946;
}

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 2019112 +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))