Details

analyze249.0ms (3%)

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)

sample1.6s (18.9%)

Results

1.3s	8256×	body	128	valid
43.0ms	359×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify285.0ms (3.5%)

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 (0.1%)

Local error

Found 3 expressions with local error:

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

series370.0ms (4.5%)

Counts

3 → 69

Calls

3 calls:

281.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
84.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite89.0ms (1.1%)

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 → 168

Calls

3 calls:

85.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
85.0ms	(-.f64 (log.f64 z) z)
85.0ms	(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

simplify297.0ms (3.6%)

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

237 → 191

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

prune176.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	183	8	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	8	192

Error

0.0b

Counts

192 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 (fma.f64 x 1/2 (*.f64 y (-.f64 (log.f64 z) z))) y)
▶	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y))
	37.4b	(fma.f64 x 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3) (pow.f64 y 3)) (fma.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z)) (-.f64 (.f64 y y) (.f64 (.f64 y (-.f64 (log.f64 z) 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))
	30.7b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	15.2b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))

Compiler

Compiled 3592 to 1423 computations (60.4% saved)

localize8.0ms (0.1%)

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))

series80.0ms (1%)

Counts

1 → 36

Calls

1 calls:

80.0ms

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

rewrite74.0ms (0.9%)

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 → 31

Calls

1 calls:

73.0ms

(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

simplify156.0ms (1.9%)

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

67 → 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

prune145.0ms (1.8%)

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
▶	0.1b	(+.f64 (fma.f64 x 1/2 (*.f64 y (-.f64 (log.f64 z) z))) y)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y))
	37.4b	(fma.f64 x 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3) (pow.f64 y 3)) (fma.f64 (.f64 y (-.f64 (log.f64 z) z)) (.f64 y (-.f64 (log.f64 z) z)) (-.f64 (.f64 y y) (.f64 (.f64 y (-.f64 (log.f64 z) 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))
	30.7b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	15.2b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))

Compiler

Compiled 3010 to 1248 computations (58.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series344.0ms (4.2%)

Counts

3 → 84

Calls

3 calls:

185.0ms	(*.f64 y (-.f64 (log.f64 z) z))
79.0ms	(+.f64 (fma.f64 x 1/2 (*.f64 y (-.f64 (log.f64 z) z))) y)
79.0ms	(fma.f64 x 1/2 (*.f64 y (-.f64 (log.f64 z) z)))

rewrite66.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
385×	`fma-def_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
198×	`fma-neg_binary64`

Counts

3 → 109

Calls

3 calls:

63.0ms	(fma.f64 x 1/2 (*.f64 y (-.f64 (log.f64 z) z)))
63.0ms	(+.f64 (fma.f64 x 1/2 (*.f64 y (-.f64 (log.f64 z) z))) y)
63.0ms	(*.f64 y (-.f64 (log.f64 z) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	217	38
2	2802	36
3	5393	36
0	0	0
1	0	0

simplify280.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

942×	`unsub-neg_binary64`
628×	`sub-neg_binary64`
606×	`fma-neg_binary64`
559×	`fma-def_binary64`
510×	`distribute-neg-in_binary64`

Counts

193 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	1217
1	149	1068
2	351	960
3	780	954
4	1759	954
5	2846	954
6	3494	954
7	4028	954
8	4418	954
9	4482	954
10	4428	954
11	4428	954
12	4427	954
13	4674	954
14	4825	954
15	4891	954
16	4894	954
17	4894	954
18	5072	954

prune295.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	243	3	246
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	246	8	254

Error

0.0b

Counts

254 → 8

Alt Table

Status	Error	Program
	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))
	15.3b	(+.f64 (fma.f64 x 1/2 (*.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)))) y)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	30.7b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	29.0b	(+.f64 (fma.f64 x 1/2 (cbrt.f64 (pow.f64 (*.f64 y (-.f64 (log.f64 z) z)) 3))) y)
▶	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y))
	12.2b	(+.f64 (fma.f64 x 1/2 (/.f64 (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) y) (+.f64 z (log.f64 z)))) y)

Compiler

Compiled 4720 to 2002 computations (57.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y)
✓	0.2b	(fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z))
✓	0.5b	(cbrt.f64 (log.f64 z))
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 z)) 2)

series1.6s (19.4%)

Counts

4 → 60

Calls

4 calls:

880.0ms	(fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y)
302.0ms	(pow.f64 (cbrt.f64 (log.f64 z)) 2)
289.0ms	(cbrt.f64 (log.f64 z))
124.0ms	(fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z))

rewrite74.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

727×	`log1p-expm1-u_binary64`
727×	`expm1-log1p-u_binary64`
308×	`prod-diff_binary64`
247×	`egg-rr`
96×	`add-sqr-sqrt_binary64`

Counts

4 → 247

Calls

4 calls:

69.0ms	(fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y)
69.0ms	(fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z))
69.0ms	(cbrt.f64 (log.f64 z))
69.0ms	(pow.f64 (cbrt.f64 (log.f64 z)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	53
1	199	29
2	1910	29
3	4883	29
0	0	0
1	0	0

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

580×	`unsub-neg_binary64`
508×	`associate-l_binary64`
467×	`associate-r_binary64`
461×	`fma-def_binary64`
386×	`neg-sub0_binary64`

Counts

307 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	541
1	152	535
2	326	496
3	910	478
4	3327	478
5	4377	478
6	5077	478

prune291.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	295	8	303

Error

0.0b

Counts

303 → 8

Alt Table

Status	Error	Program
	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))
	15.3b	(+.f64 (fma.f64 x 1/2 (*.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)))) y)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))
	30.7b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 2))
	0.8b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	29.0b	(+.f64 (fma.f64 x 1/2 (cbrt.f64 (pow.f64 (*.f64 y (-.f64 (log.f64 z) z)) 3))) y)
✓	0.4b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (cbrt.f64 (log.f64 z)) (pow.f64 (cbrt.f64 (log.f64 z)) 2) (neg.f64 z)) y))
	12.2b	(+.f64 (fma.f64 x 1/2 (/.f64 (.f64 (-.f64 (pow.f64 (log.f64 z) 2) (.f64 z z)) y) (+.f64 z (log.f64 z)))) y)

Compiler

Compiled 7606 to 3267 computations (57% saved)

regimes1.2s (14.8%)

Accuracy

Total 0.1b remaining (79%)

Threshold costs 0.1b (79%)

Counts

162 → 1

Compiler

Compiled 19309 to 12638 computations (34.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`+-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	14	14
2	18	14
3	20	14
4	21	14
5	21	14

end466.0ms (5.7%)

Compiler: Compiled 176 to 109 computations (38.1% saved)

Details

analyze249.0ms (3%)

sample1.6s (18.9%)

simplify285.0ms (3.5%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series370.0ms (4.5%)

rewrite89.0ms (1.1%)

simplify297.0ms (3.6%)

prune176.0ms (2.1%)

localize8.0ms (0.1%)

series80.0ms (1%)

rewrite74.0ms (0.9%)

simplify156.0ms (1.9%)

prune145.0ms (1.8%)

localize10.0ms (0.1%)

series344.0ms (4.2%)

rewrite66.0ms (0.8%)

simplify280.0ms (3.4%)

prune295.0ms (3.6%)

localize12.0ms (0.2%)

series1.6s (19.4%)

rewrite74.0ms (0.9%)

simplify77.0ms (0.9%)

prune291.0ms (3.5%)

regimes1.2s (14.8%)

simplify3.0ms (0%)

end466.0ms (5.7%)

Profiling