Details

analyze796.0ms (15.6%)

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 (21.9%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

869.0ms	8256×	body	128	valid
206.0ms	1913×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify8.0ms (0.2%)

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

9.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.6b	(/.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
✓	9.3b	(/.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))

simplify85.0ms (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 (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	27	9	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	9	37

Error

0.0b

Counts

37 → 9

Alt Table

Status	Error	Program
	30.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)) (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (/.f64 (.f64 a1 a2) (.f64 b1 b2))))
	13.2b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	9.3b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	9.9b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	9.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	9.8b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	11.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	31.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 710 to 255 computations (64.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.4b	(/.f64 b1 (/.f64 a2 b2))
✓	5.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

series39.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

28.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
12.0ms	(/.f64 b1 (/.f64 a2 b2))

rewrite47.0ms (0.9%)

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))

simplify261.0ms (5.1%)

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

prune261.0ms (5.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	445	4	449
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	450	8	458

Error

0.0b

Counts

458 → 8

Alt Table

Status	Error	Program
	11.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
▶	9.0b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	10.1b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (*.f64 (cbrt.f64 b1) (cbrt.f64 b1)) a2)) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 1 b2))))
	9.6b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
	11.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	9.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	31.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 8503 to 1842 computations (78.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(*.f64 b1 (/.f64 b2 a2))
✓	5.7b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))

series39.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

27.0ms	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
12.0ms	(*.f64 b1 (/.f64 b2 a2))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

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

simplify110.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
529×	`associate-/l*_binary64`
394×	`associate-*l/_binary64`
385×	`associate-/r*_binary64`
361×	`associate-*r/_binary64`

Counts

144 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1527
1	256	1398
2	952	1398
3	4087	1395
4	4343	1395
5	4779	1395
6	4961	1395
7	4965	1395

prune57.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Error

Counts

97 → 9

Alt Table

Status	Error	Program
	11.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	9.0b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	10.1b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (*.f64 (cbrt.f64 b1) (cbrt.f64 b1)) a2)) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 1 b2))))
▶	9.6b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
	11.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	9.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	11.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	31.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 1366 to 451 computations (67% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.6b	(*.f64 a1 (/.f64 a2 b2))
✓	5.6b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))

series43.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
12.0ms	(*.f64 a1 (/.f64 a2 b2))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`prod-exp_binary64`
19×	`times-frac_binary64`

Counts

2 → 81

Calls

2 calls:

7.0ms	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
6.0ms	(*.f64 a1 (/.f64 a2 b2))

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

508×	`sqr-pow_binary64`
437×	`associate-/l*_binary64`
350×	`fma-neg_binary64`
338×	`times-frac_binary64`
329×	`fma-def_binary64`

Counts

165 → 115

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	129	1812
1	296	1620
2	1059	1620
3	2649	1620
4	3164	1620
5	4121	1620
6	4595	1620
7	5316	1620

prune72.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	115	9	124

Error

Counts

124 → 9

Alt Table

Status	Error	Program
	11.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	9.0b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	10.1b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (*.f64 (cbrt.f64 b1) (cbrt.f64 b1)) a2)) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 1 b2))))
✓	9.6b	(.f64 (/.f64 1 b1) (.f64 a1 (/.f64 a2 b2)))
	11.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	9.6b	(pow.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1)) 1)
	11.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	31.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 1878 to 758 computations (59.6% saved)

regimes1.5s (30%)

Accuracy

Total 1.7b remaining (98.7%)

Threshold costs 0b (0%)

Counts

133 → 5

Compiler

Compiled 18706 to 10873 computations (41.9% saved)

bsearch4.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	164
1	46	164
2	46	164

end394.0ms (7.7%)

Compiler: Compiled 795 to 311 computations (60.9% saved)

Details

analyze796.0ms (15.6%)

sample1.1s (21.9%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series26.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify85.0ms (1.7%)

prune32.0ms (0.6%)

localize5.0ms (0.1%)

series39.0ms (0.8%)

rewrite47.0ms (0.9%)

simplify261.0ms (5.1%)

prune261.0ms (5.1%)

localize5.0ms (0.1%)

series39.0ms (0.8%)

rewrite13.0ms (0.3%)

simplify110.0ms (2.2%)

prune57.0ms (1.1%)

localize7.0ms (0.1%)

series43.0ms (0.8%)

rewrite19.0ms (0.4%)

simplify111.0ms (2.2%)

prune72.0ms (1.4%)

regimes1.5s (30%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end394.0ms (7.7%)

Profiling