Details

analyze581.0ms (8%)

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
35.1%	55%	9.9%	9
36.3%	50.9%	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)

sample339.0ms (4.6%)

Algorithm

1×

intervals

Results

10.0ms	168×	body	128	valid
8.0ms	30×	body	2048	valid
6.0ms	28×	body	1024	valid
6.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	12×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify76.0ms (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

31.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.8b	(/.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)

localize7.0ms (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)
✓	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	19.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series269.0ms (3.7%)

Counts

4 → 96

Calls

4 calls:

113.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
80.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
19×	`prod-diff_binary64`

Counts

4 → 120

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify260.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
364×	`cancel-sign-sub-inv_binary64`
248×	`distribute-rgt-neg-in_binary64`
220×	`distribute-lft-neg-in_binary64`
172×	`distribute-rgt-in_binary64`

Counts

216 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5568
1	683	4769
2	2484	4515
3	4521	4514
4	4915	4514
5	4990	4514
6	5000	4514
7	4999	4514
8	4932	4514

prune136.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	227	10	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	228	10	238

Error

4.7b

Counts

238 → 10

Alt Table

Status	Error	Program
	32.0b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	43.6b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
	34.1b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
	45.1b	(/.f64 (*.f64 -2 b_2) a)
	51.4b	(exp.f64 (-.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (log.f64 a)))
	46.5b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	32.0b	(/.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))))
▶	31.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	32.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

Compiler

Compiled 5879 to 1684 computations (71.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	19.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series76.0ms (1%)

Counts

1 → 20

Calls

1 calls:

76.0ms

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

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 45

Calls

1 calls:

13.0ms

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

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

461×	`times-frac_binary64`
381×	`associate-l_binary64`
320×	`associate-/l*_binary64`
257×	`associate-/r*_binary64`
248×	`fma-neg_binary64`

Counts

65 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	1800
1	372	1651
2	1204	1581
3	4735	1581
4	4985	1581
5	4951	1581

prune148.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	244	9	253

Error

4.7b

Counts

253 → 9

Alt Table

Status	Error	Program
▶	32.0b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
	34.1b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
	45.1b	(/.f64 (*.f64 -2 b_2) a)
	51.4b	(exp.f64 (-.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (log.f64 a)))
	42.7b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
	46.5b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	32.0b	(/.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))))
✓	31.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 6251 to 2168 computations (65.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
✓	0.6b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	10.9b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series471.0ms (6.4%)

Counts

3 → 24

Calls

3 calls:

213.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
149.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
108.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

3 → 88

Calls

3 calls:

5.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify169.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-def_binary64`
428×	`fma-neg_binary64`
291×	`cancel-sign-sub-inv_binary64`
277×	`div-sub_binary64`
219×	`associate-/r/_binary64`

Counts

112 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3125
1	530	2608
2	1783	2484
3	4376	2480
4	5049	2480

prune69.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	142	9	151

Error

0.1b

Counts

151 → 9

Alt Table

Status	Error	Program
✓	32.0b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
▶	32.1b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	45.1b	(/.f64 (*.f64 -2 b_2) a)
	42.7b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
	46.5b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	48.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	44.6b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
✓	31.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 3653 to 1069 computations (70.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
✓	0.2b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	0.6b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	10.9b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series957.0ms (13.1%)

Counts

2 → 16

Calls

2 calls:

684.0ms

(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

273.0ms

(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))

rewrite119.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

480×	`times-frac_binary64`
340×	`*-un-lft-identity_binary64`
340×	`add-sqr-sqrt_binary64`
310×	`sqrt-prod_binary64`
216×	`add-cube-cbrt_binary64`

Counts

2 → 348

Calls

2 calls:

16.0ms

(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))

5.0ms

(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

simplify463.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

348×	`associate-/r/_binary64`
334×	`associate-/l/_binary64`
315×	`fma-neg_binary64`
258×	`fma-def_binary64`
228×	`associate-*l/_binary64`

Counts

364 → 387

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	415	23735
1	918	21479
2	2982	19917
3	4122	19412
4	5058	19412

prune223.0ms (3.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	539	0	539
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	539	9	548

Error

0.1b

Counts

548 → 9

Alt Table

Status	Error	Program
✓	32.0b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
✓	32.1b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	45.1b	(/.f64 (*.f64 -2 b_2) a)
	42.7b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
	46.5b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	48.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	44.6b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
✓	31.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 23108 to 2969 computations (87.2% saved)

regimes1.1s (15.3%)

Accuracy

Total 10.3b remaining (98.1%)

Threshold costs 0b (0%)

Counts

85 → 3

Compiler

Compiled 7384 to 4070 computations (44.9% saved)

bsearch58.0ms (0.8%)

Steps

Iters	Range		Point
8	1.3507925996137721e-92	9.847339430767924e-90	3.760743366167215e-92
10	-7.316171631311603e+147	-3.2933035680497686e+137	-6.1099423946482894e+143

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	24	47
1	34	47
2	49	47
3	59	47
4	66	47
5	68	47
6	68	47

end1.0ms (0%)

Compiler: Compiled 35 to 22 computations (37.1% saved)

sample1.6s (21.6%)

Algorithm

1×

intervals

Results

347.0ms	1107×	body	2048	valid
326.0ms	5222×	body	128	valid
179.0ms	740×	body	1024	valid
137.0ms	380×	body	4096	valid
69.0ms	370×	body	512	valid
47.0ms	770×	body	128	nan
21.0ms	181×	body	256	valid
14.0ms	247×	body	128	invalid

Compiler

Compiled 196 to 119 computations (39.3% saved)

Details

analyze581.0ms (8%)

sample339.0ms (4.6%)

simplify76.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series269.0ms (3.7%)

rewrite32.0ms (0.4%)

simplify260.0ms (3.6%)

prune136.0ms (1.9%)

localize9.0ms (0.1%)

series76.0ms (1%)

rewrite17.0ms (0.2%)

simplify81.0ms (1.1%)

prune148.0ms (2%)

localize7.0ms (0.1%)

series471.0ms (6.4%)

rewrite15.0ms (0.2%)

simplify169.0ms (2.3%)

prune69.0ms (0.9%)

localize20.0ms (0.3%)

series957.0ms (13.1%)

rewrite119.0ms (1.6%)

simplify463.0ms (6.3%)

prune223.0ms (3.1%)

regimes1.1s (15.3%)

bsearch58.0ms (0.8%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.6s (21.6%)

Profiling