Details

analyze318.0ms (3.8%)

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%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	62.4%	37.6%	5
0%	56.2%	43.8%	6
6.2%	49.9%	43.8%	7
9.4%	43.7%	47%	8
14%	37.4%	48.5%	9
21.1%	30.4%	48.5%	10
24.6%	26.1%	49.3%	11
28.7%	21.6%	49.7%	12
33.4%	16.9%	49.7%	13
35.8%	14.3%	49.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.3s (16%)

Results

1.1s	8254×	body	128	valid
6.0ms	61×	body	128	invalid
1.0ms	2×	body	512	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify149.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

3353×	`fma-neg_binary64`
476×	`distribute-rgt-in_binary64`
425×	`unsub-neg_binary64`
361×	`fma-def_binary64`
308×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	12
2	36	12
3	76	12
4	131	12
5	231	12
6	342	12
7	678	12
8	1365	12
9	2068	12
10	2356	12
11	2518	12
12	2627	12
13	2660	12
14	2664	12
15	2866	12
16	2767	12
17	2779	12
18	2791	12
19	2799	12
20	2799	12
21	5311	12

prune2.0ms (0%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x (log.f64 y)) z)
✓	0.0b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
✓	0.2b	(*.f64 x (log.f64 y))

series384.0ms (4.6%)

Counts

3 → 96

Calls

3 calls:

207.0ms	(*.f64 x (log.f64 y))
94.0ms	(-.f64 (*.f64 x (log.f64 y)) z)
83.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

rewrite81.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

503×	`fma-def_binary64`
463×	`log-prod_binary64`
303×	`fma-neg_binary64`
272×	`egg-rr`
172×	`expm1-udef_binary64`

Counts

3 → 272

Calls

3 calls:

73.0ms	(-.f64 (*.f64 x (log.f64 y)) z)
73.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
73.0ms	(*.f64 x (log.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	179	27
2	2442	27
3	5093	27
0	0	0
1	0	0

simplify251.0ms (3%)

Algorithm

1×	egg-herbie

Rules

3264×	`fma-neg_binary64`
799×	`associate--r-_binary64`
593×	`fma-def_binary64`
426×	`sub-neg_binary64`
392×	`unsub-neg_binary64`

Counts

368 → 288

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	813
1	93	813
2	205	813
3	372	813
4	894	813
5	1824	813
6	1860	813
7	1754	813
8	1856	813
9	1896	813
10	1906	813
11	1959	813
12	1920	813
13	1920	813
14	4536	813
15	5250	813

prune205.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	282	6	288
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	7	289

Error

0.0b

Counts

289 → 7

Alt Table

Status	Error	Program
	29.6b	(-.f64 (-.f64 (pow.f64 (sqrt.f64 (*.f64 x (log.f64 y))) 2) z) y)
	0.4b	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 (+.f64 y z)))
	35.0b	(fma.f64 (-.f64 (pow.f64 (.f64 x (log.f64 y)) 2) (.f64 z z)) (/.f64 1 (fma.f64 x (log.f64 y) z)) (neg.f64 y))
	26.1b	(fma.f64 (sqrt.f64 (log.f64 y)) (*.f64 (sqrt.f64 (log.f64 y)) x) (neg.f64 (+.f64 y z)))
▶	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 (+.f64 y z)))
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

Compiler

Compiled 4862 to 1378 computations (71.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
	0.2b	(*.f64 x (log.f64 y))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 2)
✓	0.6b	(cbrt.f64 (*.f64 x (log.f64 y)))

series2.9s (34%)

Counts

3 → 84

Calls

3 calls:

1.5s	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
701.0ms	(cbrt.f64 (*.f64 x (log.f64 y)))
695.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 2)

rewrite58.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

528×	`log-prod_binary64`
287×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
178×	`log-pow_binary64`

Counts

3 → 91

Calls

3 calls:

56.0ms	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
56.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 2)
56.0ms	(cbrt.f64 (*.f64 x (log.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	252	29
2	2742	27
3	5006	27
0	0	0
1	0	0

simplify137.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1120×	`prod-exp_binary64`
925×	`unswap-sqr_binary64`
627×	`fma-neg_binary64`
436×	`fma-def_binary64`
175×	`times-frac_binary64`

Counts

175 → 123

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	2014
1	225	1547
2	467	1366
3	1497	944
4	4529	936
5	3556	936
6	4431	936
7	5885	936

prune210.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	196	8	204

Error

0.0b

Counts

204 → 8

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 x)) (cbrt.f64 (log.f64 y))) (neg.f64 (+.f64 y z)))
	26.1b	(fma.f64 (sqrt.f64 (log.f64 y)) (*.f64 (sqrt.f64 (log.f64 y)) x) (neg.f64 (+.f64 y z)))
	29.6b	(-.f64 (-.f64 (pow.f64 (sqrt.f64 (*.f64 x (log.f64 y))) 2) z) y)
	0.4b	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 (+.f64 y z)))
	35.0b	(fma.f64 (-.f64 (pow.f64 (.f64 x (log.f64 y)) 2) (.f64 z z)) (/.f64 1 (fma.f64 x (log.f64 y) z)) (neg.f64 y))
	0.4b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
✓	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

Compiler

Compiled 3971 to 1315 computations (66.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (*.f64 x (log.f64 y))) (cbrt.f64 x)) (cbrt.f64 (log.f64 y)))
✓	0.6b	(cbrt.f64 (log.f64 y))
✓	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 (*.f64 x (log.f64 y)))

series1.6s (18.7%)

Counts

3 → 48

Calls

3 calls:

1.1s	(.f64 (.f64 (cbrt.f64 (*.f64 x (log.f64 y))) (cbrt.f64 x)) (cbrt.f64 (log.f64 y)))
425.0ms	(cbrt.f64 (log.f64 y))
28.0ms	(cbrt.f64 x)

rewrite47.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`log1p-expm1-u_binary64`
745×	`expm1-log1p-u_binary64`
152×	`expm1-udef_binary64`
152×	`log1p-udef_binary64`
99×	`associate-r_binary64`

Counts

3 → 56

Calls

3 calls:

46.0ms	(.f64 (.f64 (cbrt.f64 (*.f64 x (log.f64 y))) (cbrt.f64 x)) (cbrt.f64 (log.f64 y)))
46.0ms	(cbrt.f64 (log.f64 y))
46.0ms	(cbrt.f64 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	186	17
2	2025	17
3	5082	17
0	0	0
1	0	0

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

721×	`associate-l_binary64`
644×	`fma-neg_binary64`
398×	`exp-sum_binary64`
359×	`log-prod_binary64`
269×	`unsub-neg_binary64`

Counts

104 → 68

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	604
1	145	572
2	283	500
3	844	416
4	3033	344
5	4347	344
6	4318	344
7	4703	344
8	4989	344
9	4859	344

prune134.0ms (1.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	138	10	148

Error

0.0b

Counts

148 → 10

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 x)) (cbrt.f64 (log.f64 y))) (neg.f64 (+.f64 y z)))
	26.1b	(fma.f64 (sqrt.f64 (log.f64 y)) (*.f64 (sqrt.f64 (log.f64 y)) x) (neg.f64 (+.f64 y z)))
	0.5b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 y)))) 3) (cbrt.f64 x)) (cbrt.f64 (log.f64 y))) (neg.f64 (+.f64 y z)))
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
	26.2b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 x)) (*.f64 (cbrt.f64 (cbrt.f64 (log.f64 y))) (cbrt.f64 (pow.f64 (log.f64 y) 2/3)))) (neg.f64 (+.f64 y z)))
	26.1b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 x)) (pow.f64 (log.f64 y) 1/3)) (neg.f64 (+.f64 y z)))
	0.4b	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 (+.f64 y z)))
	35.0b	(fma.f64 (-.f64 (pow.f64 (.f64 x (log.f64 y)) 2) (.f64 z z)) (/.f64 1 (fma.f64 x (log.f64 y) z)) (neg.f64 y))
▶	0.4b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
✓	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))

Compiler

Compiled 3927 to 1041 computations (73.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 y))) 2)
	0.6b	(cbrt.f64 (log.f64 y))
	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 (*.f64 x (log.f64 y)))

prune130.0ms (1.5%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	4	6
Picked	0	1	1
Done	0	3	3
Total	115	11	126

Error

0.0b

Counts

126 → 11

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 x)) (cbrt.f64 (log.f64 y))) (neg.f64 (+.f64 y z)))
	26.1b	(fma.f64 (sqrt.f64 (log.f64 y)) (*.f64 (sqrt.f64 (log.f64 y)) x) (neg.f64 (+.f64 y z)))
	0.5b	(fma.f64 (.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 y))) 3)) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
	0.5b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 y)))) 3) (cbrt.f64 x)) (cbrt.f64 (log.f64 y))) (neg.f64 (+.f64 y z)))
✓	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
	26.2b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 x)) (*.f64 (cbrt.f64 (cbrt.f64 (log.f64 y))) (cbrt.f64 (pow.f64 (log.f64 y) 2/3)))) (neg.f64 (+.f64 y z)))
	0.4b	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 (+.f64 y z)))
	0.5b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) (cbrt.f64 (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
✓	0.4b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
✓	0.4b	(fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 (+.f64 y z)))
	11.4b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (log.f64 y))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 4)) (neg.f64 (+.f64 y z)))

Compiler

Compiled 2836 to 968 computations (65.9% saved)

regimes217.0ms (2.6%)

Accuracy

Total 0.1b remaining (62.3%)

Threshold costs 0.1b (62.3%)

Counts

57 → 1

Compiler

Compiled 4106 to 2656 computations (35.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	21	12
3	25	12
4	27	12
5	27	12

end153.0ms (1.8%)

Compiler: Compiled 263 to 162 computations (38.4% saved)

Details

analyze318.0ms (3.8%)

sample1.3s (16%)

simplify149.0ms (1.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series384.0ms (4.6%)

rewrite81.0ms (1%)

simplify251.0ms (3%)

prune205.0ms (2.4%)

localize10.0ms (0.1%)

series2.9s (34%)

rewrite58.0ms (0.7%)

simplify137.0ms (1.6%)

prune210.0ms (2.5%)

localize13.0ms (0.2%)

series1.6s (18.7%)

rewrite47.0ms (0.6%)

simplify118.0ms (1.4%)

prune134.0ms (1.6%)

localize13.0ms (0.2%)

prune130.0ms (1.5%)

regimes217.0ms (2.6%)

simplify2.0ms (0%)

end153.0ms (1.8%)

Profiling