Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample2.0s (66.7%)

Results

1.4s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify201.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series22.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
8.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite75.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
399×	`fma-def_binary64`
203×	`fma-neg_binary64`
189×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

3 → 125

Calls

3 calls:

72.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
72.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
72.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	41
1	223	41
2	2931	39
3	5582	39

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-neg_binary64`
671×	`times-frac_binary64`
338×	`associate-/r*_binary64`
316×	`fma-def_binary64`
193×	`associate-r_binary64`

Counts

161 → 191

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	833
1	334	800
2	1017	777
3	3530	774
4	5035	774

prune114.0ms (3.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	190	2	192

Error

Counts

192 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 3913 to 2698 computations (31.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x))
✓	0.0b	(fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x)

series30.0ms (1%)

Counts

3 → 28

Calls

3 calls:

16.0ms	(log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x))
11.0ms	(/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x)
4.0ms	(fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

rewrite108.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

464×	`log-prod_binary64`
410×	`prod-diff_binary64`
179×	`egg-rr`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Counts

3 → 179

Calls

3 calls:

99.0ms	(log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x))
99.0ms	(fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
99.0ms	(/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	51
1	206	51
2	2419	51
3	4860	51
4	5188	51

simplify80.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-/r*_binary64`
503×	`associate-l_binary64`
336×	`fma-def_binary64`
323×	`div-sub_binary64`
311×	`fma-neg_binary64`

Counts

207 → 233

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	921
1	430	854
2	1368	769
3	4510	736
4	4789	736
5	5148	736

prune206.0ms (6.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	286	2	288

Error

Counts

288 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 7552 to 4988 computations (34% saved)

regimes55.0ms (1.8%)

Accuracy

Total 0.0b remaining (83.2%)

Threshold costs 0.0b (83.2%)

Counts

18 → 1

Compiler

Compiled 778 to 571 computations (26.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	20	23
2	26	23
3	30	23
4	32	23
5	31	23

end49.0ms (1.6%)

Compiler: Compiled 62 to 43 computations (30.6% saved)

Details

analyze6.0ms (0.2%)

sample2.0s (66.7%)

simplify201.0ms (6.5%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series22.0ms (0.7%)

rewrite75.0ms (2.4%)

simplify55.0ms (1.8%)

prune114.0ms (3.7%)

localize10.0ms (0.3%)

series30.0ms (1%)

rewrite108.0ms (3.5%)

simplify80.0ms (2.6%)

prune206.0ms (6.7%)

regimes55.0ms (1.8%)

simplify2.0ms (0.1%)

end49.0ms (1.6%)

Profiling