Details

analyze910.0ms (14.6%)

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)

sample1.3s (21%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

1.1s	8256×	body	128	valid
211.0ms	1863×	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

prune4.0ms (0.1%)

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

10.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.1b	(/.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
✓	9.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series28.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

28.0ms

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

rewrite55.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

556×	`log-prod_binary64`
237×	`pow2_binary64`
170×	`pow1/3_binary64`
161×	`expm1-udef_binary64`
161×	`log1p-udef_binary64`

Counts

1 → 60

Calls

1 calls:

54.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	169	10
2	2445	10
3	5004	10
0	0	0
1	0	0

simplify21.0ms (0.3%)

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

108 → 61

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	480
1	17	480
2	38	480
3	63	480
4	69	480
5	68	480
6	68	480

prune48.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	10	62

Error

0.0b

Counts

62 → 10

Alt Table

Status	Error	Program
	12.0b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.1b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.7b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
	12.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.8b	(.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (pow.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))) 2))
	35.2b	(.f64 (/.f64 (sqrt.f64 (.f64 a1 a2)) b1) (/.f64 (sqrt.f64 (*.f64 a1 a2)) b2))
	10.5b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
	10.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
▶	9.6b	(.f64 (/.f64 a1 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 2)) (/.f64 a2 (cbrt.f64 (*.f64 b1 b2))))
	11.2b	(.f64 (/.f64 a1 1) (/.f64 a2 (.f64 b1 b2)))

Compiler

Compiled 1008 to 382 computations (62.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 b1 b2)) 2)
✓	2.4b	(/.f64 a1 (pow.f64 (cbrt.f64 (*.f64 b1 b2)) 2))
✓	3.6b	(.f64 (/.f64 a1 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 2)) (/.f64 a2 (cbrt.f64 (*.f64 b1 b2))))
✓	13.4b	(cbrt.f64 (*.f64 b1 b2))

series2.1s (33.9%)

Counts

4 → 132

Calls

4 calls:

1.3s	(/.f64 a1 (pow.f64 (cbrt.f64 (*.f64 b1 b2)) 2))
405.0ms	(pow.f64 (cbrt.f64 (*.f64 b1 b2)) 2)
336.0ms	(cbrt.f64 (*.f64 b1 b2))
61.0ms	(.f64 (/.f64 a1 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 2)) (/.f64 a2 (cbrt.f64 (*.f64 b1 b2))))

rewrite79.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

681×	`log-prod_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
205×	`log-pow_binary64`
171×	`log-div_binary64`

Counts

4 → 154

Calls

4 calls:

76.0ms	(pow.f64 (cbrt.f64 (*.f64 b1 b2)) 2)
76.0ms	(/.f64 a1 (pow.f64 (cbrt.f64 (*.f64 b1 b2)) 2))
76.0ms	(.f64 (/.f64 a1 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 2)) (/.f64 a2 (cbrt.f64 (*.f64 b1 b2))))
76.0ms	(cbrt.f64 (*.f64 b1 b2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	255	37
2	3283	37
3	5799	37
0	0	0
1	0	0

simplify142.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-l_binary64`
447×	`fma-neg_binary64`
330×	`fma-def_binary64`
307×	`exp-prod_binary64`
245×	`unswap-sqr_binary64`

Counts

286 → 176

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	90	2112
1	242	2080
2	448	1960
3	1333	1620
4	4681	1488
5	4900	1440
6	4740	1440
7	5000	1440
8	4939	1440

prune149.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	211	10	221

Error

Counts

221 → 10

Alt Table

Status	Error	Program
	12.0b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.1b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.6b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.2b	(.f64 (/.f64 a1 1) (/.f64 a2 (.f64 b1 b2)))
	17.8b	(/.f64 (/.f64 (.f64 a1 (/.f64 a2 (cbrt.f64 (.f64 b1 b2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 b1 b2))) 2))
	10.8b	(.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (pow.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))) 2))
	35.2b	(.f64 (/.f64 (sqrt.f64 (.f64 a1 a2)) b1) (/.f64 (sqrt.f64 (*.f64 a1 a2)) b2))
	10.5b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
▶	10.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)

Compiler

Compiled 4210 to 1651 computations (60.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.9b	(/.f64 a1 (*.f64 b1 b2))
✓	6.4b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)

series46.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

29.0ms	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
17.0ms	(/.f64 a1 (*.f64 b1 b2))

rewrite54.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

867×	`log1p-expm1-u_binary64`
867×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`
78×	`add-cube-cbrt_binary64`

Counts

2 → 71

Calls

2 calls:

52.0ms	(/.f64 a1 (*.f64 b1 b2))
52.0ms	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	17
2	2229	17
3	5427	17
0	0	0
1	0	0

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

155 → 73

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	19	732
2	40	732
3	63	732
4	69	732
5	68	732
6	68	732

prune43.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Error

Counts

83 → 7

Alt Table

Status	Error	Program
	12.0b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.1b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	11.7b	(/.f64 (*.f64 (/.f64 a1 b1) a2) b2)
	12.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
▶	10.5b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	10.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	11.2b	(.f64 (/.f64 a1 1) (/.f64 a2 (.f64 b1 b2)))

Compiler

Compiled 923 to 354 computations (61.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.7b	(/.f64 (*.f64 a1 a2) b2)
✓	7.5b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))

series48.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
13.0ms	(/.f64 (*.f64 a1 a2) b2)

rewrite90.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

579×	`log-prod_binary64`
332×	`prod-diff_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
169×	`log-pow_binary64`

Counts

2 → 109

Calls

2 calls:

88.0ms	(/.f64 (*.f64 a1 a2) b2)
88.0ms	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	208	17
2	2767	17
3	4986	17
4	5679	17
0	0	0
1	0	0

simplify28.0ms (0.4%)

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

157 → 110

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	480
1	17	480
2	38	480
3	63	480
4	69	480
5	68	480
6	68	480

prune58.0ms (0.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	110	7	117

Error

Counts

117 → 7

Alt Table

Status	Error	Program
	12.0b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.1b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	11.7b	(/.f64 (*.f64 (/.f64 a1 b1) a2) b2)
	12.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	10.5b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	10.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	11.2b	(.f64 (/.f64 a1 1) (/.f64 a2 (.f64 b1 b2)))

Compiler

Compiled 1411 to 550 computations (61% saved)

regimes552.0ms (8.9%)

Accuracy

Total 2.2b remaining (99%)

Threshold costs 0b (0%)

Counts

26 → 5

Compiler

Compiled 3251 to 1991 computations (38.8% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	110
1	34	110
2	34	110

end388.0ms (6.2%)

Compiler: Compiled 555 to 215 computations (61.3% saved)

Details

analyze910.0ms (14.6%)

sample1.3s (21%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series28.0ms (0.5%)

rewrite55.0ms (0.9%)

simplify21.0ms (0.3%)

prune48.0ms (0.8%)

localize9.0ms (0.1%)

series2.1s (33.9%)

rewrite79.0ms (1.3%)

simplify142.0ms (2.3%)

prune149.0ms (2.4%)

localize6.0ms (0.1%)

series46.0ms (0.7%)

rewrite54.0ms (0.9%)

simplify28.0ms (0.4%)

prune43.0ms (0.7%)

localize6.0ms (0.1%)

series48.0ms (0.8%)

rewrite90.0ms (1.4%)

simplify28.0ms (0.4%)

prune58.0ms (0.9%)

regimes552.0ms (8.9%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end388.0ms (6.2%)

Profiling