Details

analyze800.0ms (12.4%)

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)

sample1.1s (17.7%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

893.0ms	8256×	body	128	valid
199.0ms	1878×	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

13.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.5b	(/.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
✓	13.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series33.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

33.0ms

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

rewrite9.0ms (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:

7.0ms

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

simplify88.0ms (1.4%)

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

prune33.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Error

0.0b

Counts

37 → 8

Alt Table

Status	Error	Program
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	9.3b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	14.1b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	11.1b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	14.1b	(.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))))
✓	13.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 657 to 226 computations (65.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.7b	(/.f64 b1 (/.f64 a2 b2))
✓	5.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

series51.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

33.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
18.0ms	(/.f64 b1 (/.f64 a2 b2))

rewrite62.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
229×	`add-sqr-sqrt_binary64`
229×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

2 → 270

Calls

2 calls:

10.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
4.0ms	(/.f64 b1 (/.f64 a2 b2))

simplify276.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

558×	`associate-/r/_binary64`
413×	`associate-/l/_binary64`
375×	`associate-*l/_binary64`
330×	`*-commutative_binary64`
328×	`associate-*r/_binary64`

Counts

354 → 449

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	452	7123
1	994	6901
2	3658	6898
3	3582	6898
4	4211	6898
5	4604	6898
6	5079	6898

prune252.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	446	3	449
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	449	8	457

Error

Counts

457 → 8

Alt Table

Status	Error	Program
	12.2b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	10.6b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
✓	9.3b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	9.1b	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (*.f64 b2 (cbrt.f64 b1))))
✓	13.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 8439 to 1810 computations (78.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 b1) (cbrt.f64 b1))
✓	0.6b	(cbrt.f64 b1)
✓	3.1b	(/.f64 a1 (*.f64 b2 (cbrt.f64 b1)))
✓	5.8b	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (*.f64 b2 (cbrt.f64 b1))))

series689.0ms (10.7%)

Counts

4 → 108

Calls

4 calls:

573.0ms	(/.f64 a1 (*.f64 b2 (cbrt.f64 b1)))
47.0ms	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (*.f64 b2 (cbrt.f64 b1))))
39.0ms	(*.f64 (cbrt.f64 b1) (cbrt.f64 b1))
30.0ms	(cbrt.f64 b1)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
35×	`add-cbrt-cube_binary64`
31×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64`

Counts

4 → 126

Calls

4 calls:

10.0ms	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (*.f64 b2 (cbrt.f64 b1))))
5.0ms	(*.f64 (cbrt.f64 b1) (cbrt.f64 b1))
4.0ms	(/.f64 a1 (*.f64 b2 (cbrt.f64 b1)))
1.0ms	(cbrt.f64 b1)

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-/l/_binary64`
461×	`unswap-sqr_binary64`
453×	`*-commutative_binary64`
215×	`fma-def_binary64`
184×	`associate-/r/_binary64`

Counts

234 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	3505
1	412	2490
2	1722	2423
3	3365	2408
4	4970	2408

prune99.0ms (1.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	215	8	223

Error

Counts

223 → 8

Alt Table

Status	Error	Program
	12.2b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	10.6b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
✓	9.3b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	9.1b	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (*.f64 b2 (cbrt.f64 b1))))
✓	13.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 4323 to 1031 computations (76.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 1 (/.f64 b1 a2))
✓	9.8b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))

series34.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
6.0ms	(/.f64 1 (/.f64 b1 a2))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

167×	`times-frac_binary64`
119×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
58×	`add-exp-log_binary64`

Counts

2 → 179

Calls

2 calls:

17.0ms	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
4.0ms	(/.f64 1 (/.f64 b1 a2))

simplify142.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

776×	`times-frac_binary64`
434×	`associate-/l/_binary64`
373×	`*-commutative_binary64`
343×	`associate-/r/_binary64`
291×	`associate-/r*_binary64`

Counts

251 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3263
1	428	2844
2	1443	2817
3	3564	2817
4	4129	2817
5	4783	2817
6	4966	2817

prune145.0ms (2.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	274	8	282

Error

Counts

282 → 8

Alt Table

Status	Error	Program
	12.2b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	10.6b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
✓	9.3b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	9.1b	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (*.f64 b2 (cbrt.f64 b1))))
✓	13.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 4890 to 1822 computations (62.7% saved)

regimes2.0s (30.6%)

Accuracy

Total 5.0b remaining (99.5%)

Threshold costs 0b (0%)

Counts

82 → 5

Compiler

Compiled 10996 to 6439 computations (41.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	95
1	44	95
2	43	95

end387.0ms (6%)

Compiler: Compiled 511 to 271 computations (47% saved)

Details

analyze800.0ms (12.4%)

sample1.1s (17.7%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series33.0ms (0.5%)

rewrite9.0ms (0.1%)

simplify88.0ms (1.4%)

prune33.0ms (0.5%)

localize5.0ms (0.1%)

series51.0ms (0.8%)

rewrite62.0ms (1%)

simplify276.0ms (4.3%)

prune252.0ms (3.9%)

localize10.0ms (0.1%)

series689.0ms (10.7%)

rewrite36.0ms (0.6%)

simplify101.0ms (1.6%)

prune99.0ms (1.5%)

localize6.0ms (0.1%)

series34.0ms (0.5%)

rewrite39.0ms (0.6%)

simplify142.0ms (2.2%)

prune145.0ms (2.3%)

regimes2.0s (30.6%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end387.0ms (6%)

Profiling