Details

analyze247.0ms (0.2%)

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%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample1.3s (0.9%)

Results

1.0s	8256×	body	128	valid
49.0ms	400×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify294.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
806×	`fma-neg_binary64`
746×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	59	16
3	115	16
4	270	14
5	514	14
6	792	14
7	1191	14
8	1435	14
9	1716	14
10	2343	14
11	2639	14
12	2704	14
13	3251	14
14	3766	14
15	3977	14
16	4124	14
17	4234	14
18	4260	14
19	4085	14
20	4111	14
21	4149	14
22	4189	14
23	4189	14
24	4189	14
25	4871	14
26	4999	14
27	4907	14

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 51 to 31 computations (39.2% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log.f64 z) z)
✓	0.0b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series293.0ms (0.2%)

Counts

3 → 69

Calls

3 calls:

201.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
87.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite97.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
425×	`log-prod_binary64`
221×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Counts

3 → 165

Calls

3 calls:

93.0ms	(-.f64 (log.f64 z) z)
93.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
93.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	188	30
2	2293	30
3	4933	30
4	4973	30
0	0	0
1	0	0

simplify306.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1274×	`unsub-neg_binary64`
805×	`distribute-neg-in_binary64`
676×	`sub-neg_binary64`
489×	`fma-def_binary64`
419×	`+-commutative_binary64`

Counts

234 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	926
1	139	819
2	345	717
3	759	717
4	2015	717
5	2532	717
6	3132	717
7	3501	717
8	3593	717
9	3688	717
10	3727	717
11	3735	717
12	3740	717
13	3967	717
14	4012	717
15	4054	717
16	4066	717
17	4084	717
18	4090	717
19	4108	717
20	4630	717
21	4712	717
22	5057	717

prune156.0ms (0.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	8	191

Error

0.0b

Counts

191 → 8

Alt Table

Status	Error	Program
	24.7b	(fma.f64 x 1/2 (/.f64 (-.f64 (.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z))) (.f64 y y)) (-.f64 (*.f64 y (-.f64 (log.f64 z) z)) y)))
	0.7b	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))
	19.9b	(fma.f64 x 1/2 (+.f64 (*.f64 (log.f64 z) y) y))
	29.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	31.5b	(fma.f64 x 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 3)))
	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	12.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) (/.f64 1 (+.f64 z (log.f64 z)))) y))
▶	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

Compiler

Compiled 3562 to 1415 computations (60.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log.f64 z) z)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

series90.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

90.0ms

(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

rewrite76.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
425×	`log-prod_binary64`
224×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Counts

1 → 30

Calls

1 calls:

75.0ms

(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	188	14
2	2294	14
3	4937	14
4	4976	14
0	0	0
1	0	0

simplify160.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-neg_binary64`
847×	`sub-neg_binary64`
705×	`unsub-neg_binary64`
450×	`fma-def_binary64`
382×	`neg-sub0_binary64`

Counts

66 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	107	530
2	281	503
3	656	443
4	1675	443
5	3078	443
6	3726	443
7	4162	443
8	4502	443
9	4718	443
10	4687	443
11	4687	443
12	4911	443

prune136.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	155	8	163

Error

0.0b

Counts

163 → 8

Alt Table

Status	Error	Program
	24.7b	(fma.f64 x 1/2 (/.f64 (-.f64 (.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z))) (.f64 y y)) (-.f64 (*.f64 y (-.f64 (log.f64 z) z)) y)))
▶	0.7b	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))
	19.9b	(fma.f64 x 1/2 (+.f64 (*.f64 (log.f64 z) y) y))
	29.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	31.5b	(fma.f64 x 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 3)))
	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	12.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) (/.f64 1 (+.f64 z (log.f64 z)))) y))
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

Compiler

Compiled 2990 to 1242 computations (58.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))
✓	0.1b	(fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y)
✓	0.5b	(cbrt.f64 (-.f64 (log.f64 z) z))
✓	0.7b	(pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3)

series23.4s (15.6%)

Counts

4 → 84

Calls

4 calls:

8.2s	(pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3)
7.6s	(fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y)
7.6s	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))
17.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))

rewrite131.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

526×	`prod-diff_binary64`
379×	`fma-udef_binary64`
253×	`fma-def_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`

Counts

4 → 194

Calls

4 calls:

127.0ms	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))
127.0ms	(fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y)
127.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))
127.0ms	(pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	235	38
2	2715	38
3	4811	38
4	4961	38
5	4875	38
0	0	0
1	0	0

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
300×	`cancel-sign-sub-inv_binary64`
264×	`fma-neg_binary64`
198×	`times-frac_binary64`
175×	`associate-/l*_binary64`

Counts

278 → 250

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2216
1	504	2041
2	1621	1749
3	4597	1487
4	4964	1487

prune205.0ms (0.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	249	1	250
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	249	9	258

Error

0.0b

Counts

258 → 9

Alt Table

Status	Error	Program
	24.7b	(fma.f64 x 1/2 (/.f64 (-.f64 (.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z))) (.f64 y y)) (-.f64 (*.f64 y (-.f64 (log.f64 z) z)) y)))
✓	0.7b	(fma.f64 x 1/2 (fma.f64 y (pow.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) 3) y))
	19.9b	(fma.f64 x 1/2 (+.f64 (*.f64 (log.f64 z) y) y))
	1.9b	(fma.f64 x 1/2 (+.f64 y (.f64 (+.f64 (/.f64 (neg.f64 (log.f64 z)) z) 1) (.f64 (neg.f64 z) y))))
	29.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 z (exp.f64 z))) (cbrt.f64 (/.f64 z (exp.f64 z))))) (log.f64 (cbrt.f64 (/.f64 z (exp.f64 z))))) y))
	31.5b	(fma.f64 x 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) 3)))
▶	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	12.4b	(fma.f64 x 1/2 (fma.f64 y (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) (/.f64 1 (+.f64 z (log.f64 z)))) y))
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))

Compiler

Compiled 5637 to 2771 computations (50.8% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) y)
✓	0.6b	(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3)

Details

analyze247.0ms (0.2%)

sample1.3s (0.9%)

simplify294.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0%)

series293.0ms (0.2%)

rewrite97.0ms (0.1%)

simplify306.0ms (0.2%)

prune156.0ms (0.1%)

localize7.0ms (0%)

series90.0ms (0.1%)

rewrite76.0ms (0.1%)

simplify160.0ms (0.1%)

prune136.0ms (0.1%)

localize10.0ms (0%)

series23.4s (15.6%)

rewrite131.0ms (0.1%)

simplify82.0ms (0.1%)

prune205.0ms (0.1%)

localize10.0ms (0%)

series2.0min (82%)

Profiling