Average Error: 64.0 → 64.0
Time: 861.0ms
Precision: binary64
\[1.9 \leq t \land t \leq 2.1\]
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]
↓
\[-1.7 \cdot 10^{+308}\]
1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}
↓
-1.7 \cdot 10^{+308}
(FPCore (t) :precision binary64 (- (* 1.7e+308 t) 1.7e+308))
↓
(FPCore (t) :precision binary64 -1.7e+308)
double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}
↓
double code(double t) {
	return -1.7e+308;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original64.0
Target0
Herbie64.0
\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)\]

Derivation

  1. Initial program 64.0

    \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308}\]

  2. Taylor expanded around 0 64.0

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

  3. Final simplification64.0

    \[\leadsto -1.7 \cdot 10^{+308}\]

Reproduce

herbie shell --seed 2021019 
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (<= 1.9 t 2.1)

  :herbie-target
  (fma 1.7e+308 t (- 1.7e+308))

  (- (* 1.7e+308 t) 1.7e+308))