Average Error: 49.1 → 0
Time: 5.3s
Precision: 64
\[1.9 \le t \le 2.1\]
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
↓
\[\left(t - 1\right) \cdot 1.7 \cdot 10^{+308}\]
1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}
↓
\left(t - 1\right) \cdot 1.7 \cdot 10^{+308}
double f(double t) {
        double r4742097 = 1.7e+308;
        double r4742098 = t;
        double r4742099 = r4742097 * r4742098;
        double r4742100 = r4742099 - r4742097;
        return r4742100;
}
↓
double f(double t) {
        double r4742101 = t;
        double r4742102 = 1.0;
        double r4742103 = r4742101 - r4742102;
        double r4742104 = 1.7e+308;
        double r4742105 = r4742103 * r4742104;
        return r4742105;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 49.1

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

  3. Applied *-un-lft-identity49.1

    \[\leadsto 1.7 \cdot 10^{+308} \cdot t - \color{blue}{1 \cdot 1.7 \cdot 10^{+308}}\]

  4. Applied *-commutative49.1

    \[\leadsto \color{blue}{t \cdot 1.7 \cdot 10^{+308}} - 1 \cdot 1.7 \cdot 10^{+308}\]

  5. Applied distribute-rgt-out--0

    \[\leadsto \color{blue}{1.7 \cdot 10^{+308} \cdot \left(t - 1\right)}\]

  6. Final simplification0

    \[\leadsto \left(t - 1\right) \cdot 1.7 \cdot 10^{+308}\]

Reproduce

herbie shell --seed 2019158 
(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))