Details

analyze644.0ms (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
34.7%	55.4%	9.9%	9
36.1%	51.1%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.5s (26.9%)

Results

644.0ms	5327×	body	128	valid
562.0ms	1191×	body	2048	valid
328.0ms	431×	body	4096	valid
299.0ms	786×	body	1024	valid
116.0ms	1009×	body	128	invalid
108.0ms	351×	body	512	valid
37.0ms	170×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
379×	`associate-/l*_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
224×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	39	18
3	69	18
4	107	18
5	178	18
6	279	18
7	382	18
8	547	18
9	587	18
10	855	18
11	1247	18
12	1117	18
13	1035	18
14	1043	18
15	1051	18
16	1077	18
17	1093	18
18	1129	18
19	1131	18
20	1143	18
21	1050	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

35.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	23.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series528.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

335.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
113.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
70.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite283.0ms (3.1%)

Algorithm

4×	egg-rewrite

Rules

168×	`egg`
100×	`egg`
66×	`egg`
25×	`egg`

Counts

4 → 359

Calls

4 calls:

84.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
71.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
56.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	175	12
2	2165	12
3	5255	12
0	7	10
1	156	10
2	1972	10
3	6334	10
0	9	15
1	206	15
2	2721	14
3	5685	14
0	10	18
1	234	18
2	3299	18
3	4945	18

simplify150.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
493×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
361×	`fma-def_binary64`
191×	`associate-*l/_binary64`

Counts

455 → 426

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	388	2175
2	1292	2133
3	4966	2133

prune388.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	418	8	426
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	419	8	427

Error

4.0b

Counts

427 → 8

Alt Table

Status	Error	Program
▶	32.7b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	37.8b	(*.f64 -1/2 (/.f64 c b_2))
	44.8b	(/.f64 (/.f64 1 (/.f64 (+.f64 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))) (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (*.f64 a c))))) a)
	36.5b	(fma.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (/.f64 1 a) (neg.f64 (/.f64 b_2 a)))
	46.4b	(/.f64 (*.f64 -2 b_2) a)
	35.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
	35.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

Compiler

Compiled 11169 to 3543 computations (68.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))
✓	0.0b	(fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))
✓	0.1b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)
✓	11.7b	(sqrt.f64 (neg.f64 (*.f64 a c)))

series696.0ms (7.5%)

Counts

4 → 38

Calls

4 calls:

283.0ms	(fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))
206.0ms	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)
188.0ms	(hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))
19.0ms	(sqrt.f64 (neg.f64 (*.f64 a c)))

rewrite335.0ms (3.6%)

Algorithm

4×	egg-rewrite

Rules

72×	`egg`
48×	`egg`
25×	`egg`
21×	`egg`

Counts

4 → 166

Calls

4 calls:

107.0ms	(hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))
93.0ms	(sqrt.f64 (neg.f64 (*.f64 a c)))
73.0ms	(fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))
60.0ms	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	6
2	1273	6
3	4965	6
4	6453	6
0	11	18
1	224	16
2	2470	16
3	4970	16
0	10	15
1	199	13
2	2044	13
3	5422	13
0	8	11
1	164	9
2	1705	9
3	4885	9
4	4869	9
5	5079	9

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
629×	`fma-neg_binary64`
422×	`associate-/l*_binary64`
371×	`associate-/r*_binary64`
310×	`fma-def_binary64`

Counts

204 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1343
1	353	1217
2	1087	1151
3	4746	1151
4	5163	1151

prune130.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	227	8	235

Error

0.0b

Counts

235 → 8

Alt Table

Status	Error	Program
	35.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
	47.3b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 c))))) a)
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	37.8b	(*.f64 -1/2 (/.f64 c b_2))
	47.9b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (.f64 (pow.f64 (.f64 (neg.f64 a) (sqrt.f64 c)) 1/2) (sqrt.f64 (sqrt.f64 c))))) a)
	36.5b	(fma.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (/.f64 1 a) (neg.f64 (/.f64 b_2 a)))
	46.7b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))))) a)
▶	35.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

Compiler

Compiled 4801 to 2131 computations (55.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series96.0ms (1%)

Counts

1 → 20

Calls

1 calls:

96.0ms

(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))

rewrite97.0ms (1.1%)

Algorithm

1×	egg-rewrite

Rules

62× egg

Counts

1 → 62

Calls

1 calls:

96.0ms

(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	272	18
2	3576	18
3	5232	18

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
239×	`associate-/l*_binary64`
217×	`associate-r_binary64`

Counts

82 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	204	642
2	668	624
3	3419	624
4	4941	624

prune256.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	421	1	422
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	422	8	430

Error

0.0b

Counts

430 → 8

Alt Table

Status	Error	Program
	35.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
	47.3b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 c))))) a)
✓	35.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
▶	35.1b	(.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) a))
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	37.8b	(*.f64 -1/2 (/.f64 c b_2))
	47.9b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (.f64 (pow.f64 (.f64 (neg.f64 a) (sqrt.f64 c)) 1/2) (sqrt.f64 (sqrt.f64 c))))) a)
	46.7b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))))) a)

Compiler

Compiled 11620 to 4206 computations (63.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

prune254.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	426	0	426
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	426	8	434

Error

0.0b

Counts

434 → 8

Alt Table

Status	Error	Program
	35.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
	47.3b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 c))))) a)
✓	35.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
✓	35.1b	(.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) a))
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	37.8b	(*.f64 -1/2 (/.f64 c b_2))
	47.9b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (.f64 (pow.f64 (.f64 (neg.f64 a) (sqrt.f64 c)) 1/2) (sqrt.f64 (sqrt.f64 c))))) a)
	46.7b	(/.f64 (fma.f64 -1 b_2 (hypot.f64 b_2 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))))) a)

Compiler

Compiled 11887 to 4319 computations (63.7% saved)

regimes2.3s (25.3%)

Accuracy

Total 11.3b remaining (98.4%)

Threshold costs 0b (0%)

Counts

165 → 5

Compiler

Compiled 14396 to 8374 computations (41.8% saved)

bsearch157.0ms (1.7%)

Steps

Iters	Range		Point
10	122740712592313.53	7.731034386695147e+28	124431463817995.98
9	8.87225695244139e-93	1.4387716706883634e-87	1.547379492825384e-89
8	6.615340987126152e-133	3.4333066508345306e-128	2.9407118485521444e-128
5	-7.706913201840932e+152	-2.175060296372933e+152	-2.23401914471045e+152

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	94
1	54	94
2	67	94
3	76	94
4	81	94
5	82	94
6	81	94

end110.0ms (1.2%)

Compiler: Compiled 270 to 154 computations (43% saved)

Details

analyze644.0ms (7%)

sample2.5s (26.9%)

simplify92.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series528.0ms (5.7%)

rewrite283.0ms (3.1%)

simplify150.0ms (1.6%)

prune388.0ms (4.2%)

localize9.0ms (0.1%)

series696.0ms (7.5%)

rewrite335.0ms (3.6%)

simplify84.0ms (0.9%)

prune130.0ms (1.4%)

localize11.0ms (0.1%)

series96.0ms (1%)

rewrite97.0ms (1.1%)

simplify58.0ms (0.6%)

prune256.0ms (2.8%)

localize10.0ms (0.1%)

prune254.0ms (2.7%)

regimes2.3s (25.3%)

bsearch157.0ms (1.7%)

simplify5.0ms (0.1%)

end110.0ms (1.2%)

Profiling