Details

analyze88.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
37.5%	43.7%	18.8%	7
50%	31.2%	18.8%	8
56.2%	20.3%	23.5%	9
61.7%	14.8%	23.5%	10
64.4%	9.8%	25.9%	11
66.9%	7.2%	25.9%	12
68.2%	4.8%	27%	13
69.4%	3.6%	27%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample741.0ms (21.8%)

Symmetry

(sort a b)

Results

688.0ms	8256×	body	128	valid
13.0ms	162×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

284×	`fma-def_binary64`
31×	`associate-l_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`
19×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	21	12
2	59	12
3	122	12
4	192	12
5	260	12
6	323	12
7	372	12
8	517	12
9	601	12

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

16.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.2b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
▶	16.0b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))

Compiler

Compiled 58 to 33 computations (43.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 (.f64 (*.f64 a a) b) b)
✓	10.1b	(.f64 (.f64 a a) b)

series18.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (*.f64 a a) b) b)
7.0ms	(.f64 (.f64 a a) b)

rewrite33.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`log1p-expm1-u_binary64`
509×	`expm1-log1p-u_binary64`
455×	`unpow-prod-down_binary64`
321×	`log-prod_binary64`
151×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	121	14
2	1488	14

Stop Event

1×	node limit

Counts

2 → 34

Calls

2 calls:

32.0ms	(.f64 (.f64 (*.f64 a a) b) b)
32.0ms	(.f64 (.f64 a a) b)

simplify98.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

2154×	`associate-l_binary64`
764×	`sqr-pow_binary64`
304×	`unswap-sqr_binary64`
257×	`pow-sqr_binary64`
187×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	408
1	18	408
2	39	408
3	108	408
4	483	408
5	1067	408
6	1133	408
7	1233	408
8	1353	408
9	1475	408
10	1622	408
11	1786	408
12	1975	408
13	2188	408
14	2418	408
15	2662	408
16	2927	408
17	3206	408
18	3506	408
19	3820	408

Stop Event

1×	node limit

Counts

82 → 38

prune28.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	5	38
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

0.1b

Counts

40 → 7

Alt Table

Status	Error	Program
	5.4b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	23.2b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
✓	16.0b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	24.2b	(neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 a b) 2) 3)))
▶	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	1.2b	(neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2) 3))
	18.9b	(neg.f64 (.f64 (pow.f64 (.f64 a (sqrt.f64 b)) 2) b))

Compiler

Compiled 539 to 314 computations (41.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 a b) 2)

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(pow.f64 (*.f64 a b) 2)

rewrite31.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

471×	`log1p-expm1-u_binary64`
471×	`expm1-log1p-u_binary64`
367×	`unpow-prod-down_binary64`
262×	`log-prod_binary64`
142×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	124	7
2	1364	7

Stop Event

1×	node limit

Counts

1 → 50

Calls

1 calls:

30.0ms

(pow.f64 (*.f64 a b) 2)

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-l_binary64`
564×	`sqr-pow_binary64`
505×	`associate-r_binary64`
482×	`*-commutative_binary64`
263×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	240
1	16	240
2	37	240
3	103	240
4	432	240
5	2343	240
6	2435	240
7	2636	240
8	2834	240
9	3072	240
10	3391	240
11	4063	240
12	4557	240

Stop Event

1×	node limit

Counts

74 → 52

prune43.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	50	9	59

Error

0.0b

Counts

59 → 9

Alt Table

Status	Error	Program
	5.4b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	23.2b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
✓	16.0b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	23.8b	(neg.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 a b)) 3) (sqrt.f64 (*.f64 a b))))
	23.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 a b)) (.f64 (sqrt.f64 (.f64 a b)) (*.f64 a b))))
▶	0.8b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b))))
	5.8b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
✓	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	18.9b	(neg.f64 (.f64 (pow.f64 (.f64 a (sqrt.f64 b)) 2) b))

Compiler

Compiled 822 to 436 computations (47% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b)))
✓	0.3b	(.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b))
✓	0.4b	(pow.f64 (cbrt.f64 (*.f64 a b)) 2)
✓	12.1b	(cbrt.f64 (*.f64 a b))

series1.1s (33.5%)

Counts

4 → 96

Calls

4 calls:

469.0ms	(.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b))
321.0ms	(cbrt.f64 (*.f64 a b))
309.0ms	(pow.f64 (cbrt.f64 (*.f64 a b)) 2)
41.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b)))

rewrite41.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`log1p-expm1-u_binary64`
667×	`expm1-log1p-u_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`
126×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	183	31
2	2096	31

Stop Event

1×	node limit

Counts

4 → 77

Calls

4 calls:

40.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b)))
40.0ms	(.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b))
40.0ms	(pow.f64 (cbrt.f64 (*.f64 a b)) 2)
40.0ms	(cbrt.f64 (*.f64 a b))

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-l_binary64`
339×	`fma-def_binary64`
272×	`unswap-sqr_binary64`
179×	`distribute-rgt-in_binary64`
176×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1592
1	203	1552
2	487	1384
3	1599	1048

Stop Event

1×	node limit

Counts

173 → 101

prune100.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	133	9	142

Error

0.0b

Counts

142 → 9

Alt Table

Status	Error	Program
	17.1b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	23.2b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
▶	0.6b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b))))
	5.4b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	0.7b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 b)) (*.f64 a b))))
✓	16.0b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	5.8b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
✓	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	18.9b	(neg.f64 (.f64 (pow.f64 (.f64 a (sqrt.f64 b)) 2) b))

Compiler

Compiled 2679 to 1195 computations (55.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (cbrt.f64 (.f64 a b)) (*.f64 a b))
	0.3b	(pow.f64 (*.f64 a b) 2)
	12.1b	(cbrt.f64 (*.f64 a b))
✓	20.6b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series438.0ms (12.9%)

Counts

1 → 24

Calls

1 calls:

438.0ms

(cbrt.f64 (pow.f64 (*.f64 a b) 2))

rewrite33.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`log1p-expm1-u_binary64`
532×	`expm1-log1p-u_binary64`
471×	`unpow-prod-down_binary64`
290×	`log-prod_binary64`
158×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	142	9
2	1556	9

Stop Event

1×	node limit

Counts

1 → 54

Calls

1 calls:

32.0ms

(cbrt.f64 (pow.f64 (*.f64 a b) 2))

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

302×	`fma-neg_binary64`
287×	`exp-prod_binary64`
284×	`exp-sum_binary64`
224×	`fma-def_binary64`
175×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	408
1	108	384
2	270	312
3	742	288
4	2496	216

Stop Event

1×	node limit

Counts

78 → 61

prune134.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	168	9	177

Error

0.0b

Counts

177 → 9

Alt Table

Status	Error	Program
	17.1b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	23.2b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
	0.6b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (.f64 (.f64 (cbrt.f64 (/.f64 a (/.f64 -1 b))) (cbrt.f64 -1)) (*.f64 a b))))
✓	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	5.4b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	0.7b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 b)) (*.f64 a b))))
✓	16.0b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	5.8b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	18.9b	(neg.f64 (.f64 (pow.f64 (.f64 a (sqrt.f64 b)) 2) b))

Compiler

Compiled 3629 to 1571 computations (56.7% saved)

regimes148.0ms (4.3%)

Accuracy

Total 0.3b remaining (87.6%)

Threshold costs 0.3b (87.6%)

Counts

36 → 1

Compiler

Compiled 3040 to 1844 computations (39.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
2	14	9
3	15	9

Stop Event

1×

saturated

end99.0ms (2.9%)

Remove: (sort a b)
Compiler: Compiled 143 to 96 computations (32.9% saved)

Details

analyze88.0ms (2.6%)

sample741.0ms (21.8%)

simplify11.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series18.0ms (0.5%)

rewrite33.0ms (1%)

simplify98.0ms (2.9%)

prune28.0ms (0.8%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite31.0ms (0.9%)

simplify67.0ms (2%)

prune43.0ms (1.3%)

localize7.0ms (0.2%)

series1.1s (33.5%)

rewrite41.0ms (1.2%)

simplify44.0ms (1.3%)

prune100.0ms (2.9%)

localize10.0ms (0.3%)

series438.0ms (12.9%)

rewrite33.0ms (1%)

simplify28.0ms (0.8%)

prune134.0ms (3.9%)

regimes148.0ms (4.3%)

simplify3.0ms (0.1%)

end99.0ms (2.9%)

Profiling