Average Error: 64.0 → 0
Time: 640.0ms
Precision: 64
\[1.8999999999999999 \le t \le 2.10000000000000009\]
\[1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}\]
↓
\[\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308} \cdot 1, t, -1.6999999999999999 \cdot 10^{308}\right)\]
1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}
↓
\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308} \cdot 1, t, -1.6999999999999999 \cdot 10^{308}\right)
double code(double t) {
	return ((double) (((double) (1.7e+308 * t)) - 1.7e+308));
}
↓
double code(double t) {
	return ((double) fma(((double) (1.7e+308 * 1.0)), t, ((double) -(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
Herbie0
\[\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -1.6999999999999999 \cdot 10^{308}\right)\]

Derivation

  1. Initial program 64.0

    \[1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity64.0

    \[\leadsto 1.6999999999999999 \cdot 10^{308} \cdot \color{blue}{\left(1 \cdot t\right)} - 1.6999999999999999 \cdot 10^{308}\]

  4. Applied associate-*r*64.0

    \[\leadsto \color{blue}{\left(1.6999999999999999 \cdot 10^{308} \cdot 1\right) \cdot t} - 1.6999999999999999 \cdot 10^{308}\]

  5. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308} \cdot 1, t, -1.6999999999999999 \cdot 10^{308}\right)}\]

  6. Final simplification0

    \[\leadsto \mathsf{fma}\left(1.6999999999999999 \cdot 10^{308} \cdot 1, t, -1.6999999999999999 \cdot 10^{308}\right)\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(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))