Details

analyze856.0ms (13%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	81.1%	0.2%	9
21.8%	78%	0.2%	10
25%	74.9%	0.2%	11
34.7%	64.9%	0.4%	12
47.2%	51.9%	0.9%	13
49%	49.2%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.2s (18.1%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

933.0ms	8256×	body	128	valid
215.0ms	1933×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	63	10
4	69	10
5	68	10
6	68	10

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

12.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	12.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series48.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

48.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`

Counts

1 → 23

Calls

1 calls:

4.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r*_binary64`
476×	`associate-l_binary64`
457×	`associate-*l/_binary64`
355×	`associate-*r/_binary64`
344×	`associate-r_binary64`

Counts

71 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	859
1	161	754
2	820	754
3	3799	754
4	4127	754
5	4478	754
6	4861	754
7	5308	754

prune30.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	8	37

Error

0.0b

Counts

37 → 8

Alt Table

Status	Error	Program
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.7b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	12.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.9b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
▶	11.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	31.1b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
	13.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))))

Compiler

Compiled 692 to 241 computations (65.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

series28.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

28.0ms

(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

1 → 52

Calls

1 calls:

8.0ms

(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

648×	`associate-*l/_binary64`
573×	`associate-*r/_binary64`
489×	`associate-l_binary64`
469×	`associate-/l*_binary64`
389×	`associate-r_binary64`

Counts

100 → 81

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	113	1295
1	308	1187
2	960	1187
3	3807	1187
4	4046	1187
5	4634	1187
6	4940	1187
7	4956	1187
8	4976	1187

prune80.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	81	8	89

Error

0.0b

Counts

89 → 8

Alt Table

Status	Error	Program
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.3b	(.f64 a1 (.f64 (/.f64 1 b1) (/.f64 a2 b2)))
	12.7b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	11.5b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2)))
	12.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.9b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
✓	11.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.5b	(/.f64 (.f64 a1 a2) (.f64 b2 b1))

Compiler

Compiled 1345 to 388 computations (71.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 a1) (cbrt.f64 a1))
✓	0.6b	(cbrt.f64 a1)
✓	3.8b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2)))
✓	7.8b	(*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2))

series728.0ms (11.1%)

Counts

4 → 120

Calls

4 calls:

613.0ms	(*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2))
47.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2)))
38.0ms	(*.f64 (cbrt.f64 a1) (cbrt.f64 a1))
30.0ms	(cbrt.f64 a1)

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-exp-log_binary64`
67×	`add-cbrt-cube_binary64`
62×	`add-sqr-sqrt_binary64`
60×	`prod-exp_binary64`
44×	`div-exp_binary64`

Counts

4 → 185

Calls

4 calls:

12.0ms	(*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2))
10.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2)))
4.0ms	(*.f64 (cbrt.f64 a1) (cbrt.f64 a1))
1.0ms	(cbrt.f64 a1)

simplify153.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-/r/_binary64`
326×	`associate-l_binary64`
321×	`fma-neg_binary64`
312×	`log-prod_binary64`
271×	`cube-prod_binary64`

Counts

305 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	246	4077
1	559	3489
2	2301	3422
3	3744	3415
4	4794	3415
5	4979	3415

prune148.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	304	9	313

Error

Counts

313 → 9

Alt Table

Status	Error	Program
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.3b	(.f64 a1 (.f64 (/.f64 1 b1) (/.f64 a2 b2)))
	12.7b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	11.5b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2)))
	12.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.9b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
▶	10.3b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2)))
✓	11.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.5b	(/.f64 (.f64 a1 a2) (.f64 b2 b1))

Compiler

Compiled 7077 to 2004 computations (71.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 a2)
✓	2.5b	(.f64 (/.f64 (cbrt.f64 a1) b1) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))
✓	3.8b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2)))
✓	5.2b	(.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2))

series1.6s (24.8%)

Counts

4 → 144

Calls

4 calls:

925.0ms	(.f64 (/.f64 (cbrt.f64 a1) b1) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))
619.0ms	(.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2))
56.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2)))
34.0ms	(cbrt.f64 a2)

rewrite98.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

366×	`add-exp-log_binary64`
215×	`prod-exp_binary64`
153×	`add-cbrt-cube_binary64`
138×	`cbrt-unprod_binary64`
100×	`div-exp_binary64`

Counts

4 → 236

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2)))
13.0ms	(.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2))
8.0ms	(.f64 (/.f64 (cbrt.f64 a1) b1) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))
1.0ms	(cbrt.f64 a2)

simplify182.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

556×	`associate-l_binary64`
555×	`associate-r_binary64`
471×	`log-prod_binary64`
280×	`*-commutative_binary64`
272×	`unswap-sqr_binary64`

Counts

380 → 331

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	8552
1	774	5027
2	3310	4825
3	4386	4825
4	5020	4825

prune182.0ms (2.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	367	9	376

Error

Counts

376 → 9

Alt Table

Status	Error	Program
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.3b	(.f64 a1 (.f64 (/.f64 1 b1) (/.f64 a2 b2)))
	12.7b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	11.5b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (*.f64 (/.f64 (cbrt.f64 a1) b1) (/.f64 a2 b2)))
	12.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.9b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
✓	10.3b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) 1) (.f64 (.f64 (/.f64 (cbrt.f64 a1) b1) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))) (/.f64 (cbrt.f64 a2) b2)))
✓	11.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.5b	(/.f64 (.f64 a1 a2) (.f64 b2 b1))

Compiler

Compiled 11418 to 2688 computations (76.5% saved)

regimes640.0ms (9.7%)

Accuracy

Total 2.5b remaining (98.8%)

Threshold costs 0b (0%)

Counts

30 → 5

Compiler

Compiled 4305 to 2404 computations (44.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	134
1	42	134
2	41	134

end278.0ms (4.2%)

Remove: (sort b1 b2)
Compiler: Compiled 870 to 326 computations (62.5% saved)

Details

analyze856.0ms (13%)

sample1.2s (18.1%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series48.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify82.0ms (1.2%)

prune30.0ms (0.5%)

localize5.0ms (0.1%)

series28.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify116.0ms (1.8%)

prune80.0ms (1.2%)

localize10.0ms (0.2%)

series728.0ms (11.1%)

rewrite47.0ms (0.7%)

simplify153.0ms (2.3%)

prune148.0ms (2.2%)

localize13.0ms (0.2%)

series1.6s (24.8%)

rewrite98.0ms (1.5%)

simplify182.0ms (2.8%)

prune182.0ms (2.8%)

regimes640.0ms (9.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end278.0ms (4.2%)

Profiling