Details

analyze829.0ms (17.1%)

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 (22.8%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

871.0ms	8256×	body	128	valid
194.0ms	1887×	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

9.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.6b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series26.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

26.0ms

(/.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))

simplify84.0ms (1.7%)

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

prune32.0ms (0.7%)

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
	11.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	9.5b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	9.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	10.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	10.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	10.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	30.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
✓	9.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 639 to 224 computations (64.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.8b	(/.f64 (*.f64 a1 a2) b1)
✓	7.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series42.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
11.0ms	(/.f64 (*.f64 a1 a2) b1)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

5.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
3.0ms	(/.f64 (*.f64 a1 a2) b1)

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Rules

821×	`associate-/l*_binary64`
608×	`associate-/l/_binary64`
389×	`associate-*l/_binary64`
362×	`associate-/r*_binary64`
291×	`associate-*r/_binary64`

Counts

121 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	127	1639
1	304	1510
2	967	1510
3	4038	1510
4	4410	1510
5	4842	1510
6	5018	1510

prune78.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	99	9	108

Error

Counts

108 → 9

Alt Table

Status	Error	Program
	31.7b	(/.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) b1)) (/.f64 b2 (sqrt.f64 (/.f64 (.f64 a1 a2) b1))))
	11.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	10.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	9.7b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	10.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	30.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
▶	9.5b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
	24.9b	(/.f64 (*.f64 (/.f64 a1 (sqrt.f64 b2)) (/.f64 a2 b1)) (sqrt.f64 b2))
	10.5b	(/.f64 (/.f64 a1 1) (/.f64 b2 (/.f64 a2 b1)))

Compiler

Compiled 1608 to 475 computations (70.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	2.8b	(/.f64 (*.f64 a1 a2) b1)
✓	7.0b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)

series27.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

27.0ms

(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
83×	`*-un-lft-identity_binary64`
83×	`add-sqr-sqrt_binary64`
83×	`add-cube-cbrt_binary64`
25×	`associate-/l*_binary64`

Counts

1 → 127

Calls

1 calls:

8.0ms

(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)

simplify128.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

843×	`associate-/l*_binary64`
338×	`associate-/r*_binary64`
332×	`associate-*l/_binary64`
308×	`associate-/r/_binary64`
297×	`associate-l_binary64`

Counts

175 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	167	2902
1	302	2788
2	911	2788
3	3494	2788
4	3894	2788
5	4367	2788
6	5005	2788

prune130.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	214	9	223

Error

Counts

223 → 9

Alt Table

Status	Error	Program
	31.7b	(/.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) b1)) (/.f64 b2 (sqrt.f64 (/.f64 (.f64 a1 a2) b1))))
	11.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	10.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
▶	9.7b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	10.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	30.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
✓	9.5b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
	24.9b	(/.f64 (*.f64 (/.f64 a1 (sqrt.f64 b2)) (/.f64 a2 b1)) (sqrt.f64 b2))
	10.5b	(/.f64 (/.f64 a1 1) (/.f64 b2 (/.f64 a2 b1)))

Compiler

Compiled 4165 to 1681 computations (59.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 b1) b2)
✓	9.4b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))

series34.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

26.0ms	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
7.0ms	(/.f64 (/.f64 1 b1) b2)

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`times-frac_binary64`
106×	`add-exp-log_binary64`
93×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`

Counts

2 → 176

Calls

2 calls:

16.0ms	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
5.0ms	(/.f64 (/.f64 1 b1) b2)

simplify147.0ms (3%)

Algorithm

1×	egg-herbie

Rules

413×	`unswap-sqr_binary64`
407×	`associate-/r/_binary64`
404×	`*-commutative_binary64`
368×	`associate-/r*_binary64`
319×	`sqr-pow_binary64`

Counts

248 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3471
1	399	3103
2	1588	3091
3	2613	3091
4	3184	3091
5	3960	3091
6	5072	3091

prune152.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	247	9	256

Error

Counts

256 → 9

Alt Table

Status	Error	Program
	31.7b	(/.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) b1)) (/.f64 b2 (sqrt.f64 (/.f64 (.f64 a1 a2) b1))))
	11.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	10.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	9.7b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	10.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	30.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
✓	9.5b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
	24.9b	(/.f64 (*.f64 (/.f64 a1 (sqrt.f64 b2)) (/.f64 a2 b1)) (sqrt.f64 b2))
	10.5b	(/.f64 (/.f64 a1 1) (/.f64 b2 (/.f64 a2 b1)))

Compiler

Compiled 4920 to 2542 computations (48.3% saved)

regimes1.3s (26.5%)

Accuracy

Total 2.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts

72 → 5

Compiler

Compiled 9181 to 5535 computations (39.7% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	122
1	37	122
2	36	122

end533.0ms (11%)

Compiler: Compiled 645 to 245 computations (62% saved)

Details

analyze829.0ms (17.1%)

sample1.1s (22.8%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series26.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify84.0ms (1.7%)

prune32.0ms (0.7%)

localize5.0ms (0.1%)

series42.0ms (0.9%)

rewrite12.0ms (0.2%)

simplify99.0ms (2%)

prune78.0ms (1.6%)

localize6.0ms (0.1%)

series27.0ms (0.6%)

rewrite23.0ms (0.5%)

simplify128.0ms (2.6%)

prune130.0ms (2.7%)

localize7.0ms (0.1%)

series34.0ms (0.7%)

rewrite39.0ms (0.8%)

simplify147.0ms (3%)

prune152.0ms (3.1%)

regimes1.3s (26.5%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end533.0ms (11%)

Profiling