Details

analyze775.0ms (19.4%)

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 (27.7%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

841.0ms	8256×	body	128	valid
213.0ms	1768×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify7.0ms (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

11.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.4b	(/.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
✓	11.1b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series29.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

29.0ms

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

rewrite6.0ms (0.2%)

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:

5.0ms

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

simplify88.0ms (2.2%)

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

prune32.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	7	37

Error

0.0b

Counts

37 → 7

Alt Table

Status	Error	Program
	12.2b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	10.8b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	13.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	12.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	11.5b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	13.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 612 to 217 computations (64.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.0b	(/.f64 (*.f64 a1 a2) b1)
✓	6.5b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series40.0ms (1%)

Counts

2 → 48

Calls

2 calls:

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

rewrite12.0ms (0.3%)

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)

simplify97.0ms (2.4%)

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

prune65.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	98	9	107

Error

Counts

107 → 9

Alt Table

Status	Error	Program
▶	9.6b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.0b	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
	12.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	25.4b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 b2)) a2) (/.f64 (/.f64 1 (sqrt.f64 b2)) b1))
✓	10.8b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	13.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	11.5b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	13.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 1561 to 460 computations (70.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 a1 (/.f64 b1 a2))
✓	6.5b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)

series38.0ms (1%)

Counts

2 → 84

Calls

2 calls:

26.0ms	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
12.0ms	(/.f64 a1 (/.f64 b1 a2))

rewrite46.0ms (1.1%)

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`
47×	`associate-/l*_binary64`

Counts

2 → 270

Calls

2 calls:

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

simplify263.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-/l/_binary64`
604×	`*-commutative_binary64`
427×	`associate-r_binary64`
300×	`associate-/r*_binary64`
294×	`associate-/l*_binary64`

Counts

354 → 421

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	454	7058
1	1063	6866
2	3065	6854
3	3910	6854
4	4419	6854
5	4764	6854
6	5080	6854

prune179.0ms (4.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	419	2	421
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	422	8	430

Error

Counts

430 → 8

Alt Table

Status	Error	Program
	13.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	11.0b	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
▶	10.4b	(/.f64 a1 (*.f64 b2 (/.f64 b1 a2)))
	12.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
✓	9.6b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	10.8b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	11.5b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))

Compiler

Compiled 7953 to 1737 computations (78.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.7b	(*.f64 b2 (/.f64 b1 a2))
✓	8.3b	(/.f64 a1 (*.f64 b2 (/.f64 b1 a2)))

series38.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

26.0ms	(/.f64 a1 (*.f64 b2 (/.f64 b1 a2)))
12.0ms	(*.f64 b2 (/.f64 b1 a2))

rewrite12.0ms (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 b2 (/.f64 b1 a2))
4.0ms	(/.f64 a1 (*.f64 b2 (/.f64 b1 a2)))

simplify112.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

957×	`times-frac_binary64`
528×	`associate-/l*_binary64`
381×	`associate-/r*_binary64`
378×	`associate-*l/_binary64`
356×	`associate-*r/_binary64`

Counts

144 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1527
1	256	1398
2	948	1395
3	4096	1395
4	4385	1395
5	4840	1395
6	4998	1395
7	4939	1395

prune43.0ms (1.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	87	7	94

Error

Counts

94 → 7

Alt Table

Status	Error	Program
	9.6b	(/.f64 (/.f64 a1 b2) (/.f64 b1 a2))
	10.3b	(.f64 (/.f64 a1 (.f64 b2 b1)) a2)
	13.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
✓	10.4b	(/.f64 a1 (*.f64 b2 (/.f64 b1 a2)))
✓	10.8b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	9.6b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	11.5b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))

Compiler

Compiled 1175 to 346 computations (70.6% saved)

regimes623.0ms (15.6%)

Accuracy

Total 2.7b remaining (99.1%)

Threshold costs 0b (0%)

Counts

43 → 5

Compiler

Compiled 5374 to 3140 computations (41.6% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	110
1	31	110
2	31	110

end352.0ms (8.8%)

Compiler: Compiled 553 to 213 computations (61.5% saved)

Details

analyze775.0ms (19.4%)

sample1.1s (27.7%)

simplify7.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series29.0ms (0.7%)

rewrite6.0ms (0.2%)

simplify88.0ms (2.2%)

prune32.0ms (0.8%)

localize5.0ms (0.1%)

series40.0ms (1%)

rewrite12.0ms (0.3%)

simplify97.0ms (2.4%)

prune65.0ms (1.6%)

localize5.0ms (0.1%)

series38.0ms (1%)

rewrite46.0ms (1.1%)

simplify263.0ms (6.6%)

prune179.0ms (4.5%)

localize5.0ms (0.1%)

series38.0ms (0.9%)

rewrite12.0ms (0.3%)

simplify112.0ms (2.8%)

prune43.0ms (1.1%)

regimes623.0ms (15.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end352.0ms (8.8%)

Profiling