Details

analyze92.0ms (2.4%)

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)

sample753.0ms (19.3%)

Symmetry

(sort a b)

Results

704.0ms	8256×	body	128	valid
13.0ms	152×	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

16.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.7b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
▶	16.3b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))

Compiler

Compiled 58 to 33 computations (43.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.8b	(.f64 (.f64 (*.f64 a a) b) b)
✓	9.8b	(.f64 (.f64 a a) b)

series17.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 (.f64 (*.f64 a a) b) b)
7.0ms	(.f64 (.f64 a a) b)

rewrite33.0ms (0.9%)

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:

33.0ms	(.f64 (.f64 (*.f64 a a) b) b)
33.0ms	(.f64 (.f64 a a) b)

simplify98.0ms (2.5%)

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

prune30.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	31	7	38
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	31	9	40

Error

0.1b

Counts

40 → 9

Alt Table

Status	Error	Program
	28.8b	(neg.f64 (exp.f64 (.f64 2 (log.f64 (.f64 a b)))))
	21.6b	(neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 a b) 2) 3)))
▶	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	1.3b	(neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2) 3))
	23.4b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (*.f64 a b)) 3)) b))
	20.9b	(neg.f64 (.f64 (pow.f64 (.f64 a (sqrt.f64 b)) 2) b))
	20.7b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
✓	16.3b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	6.1b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 585 to 348 computations (40.5% 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)

rewrite30.0ms (0.8%)

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:

29.0ms

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

simplify68.0ms (1.7%)

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

prune49.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	48	13	61

Error

0.0b

Counts

61 → 13

Alt Table

Status	Error	Program
	20.7b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
	2.9b	(neg.f64 (.f64 (pow.f64 (.f64 b (pow.f64 (cbrt.f64 a) 2)) 2) (pow.f64 (cbrt.f64 a) 2)))
✓	16.3b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	18.4b	(neg.f64 (.f64 (pow.f64 (.f64 a (cbrt.f64 (.f64 b b))) 2) (cbrt.f64 (.f64 b b))))
	21.6b	(neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 a b) 2) 3)))
✓	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
▶	1.3b	(neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2) 3))
	23.4b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (*.f64 a b)) 3)) b))
	6.1b	(neg.f64 (.f64 (pow.f64 (.f64 (*.f64 a b) a) 1) b))
	27.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 a b)) (.f64 (sqrt.f64 (.f64 a b)) (*.f64 a b))))
	15.2b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2) (cbrt.f64 (pow.f64 (*.f64 a b) 4))))
	50.1b	(neg.f64 (.f64 a (pow.f64 (.f64 (sqrt.f64 a) b) 2)))
	4.3b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))

Compiler

Compiled 928 to 524 computations (43.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2) 3)
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 a b)) 2)
✓	9.5b	(cbrt.f64 (*.f64 a b))

series1.0s (26.5%)

Counts

3 → 72

Calls

3 calls:

370.0ms	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2) 3)
347.0ms	(cbrt.f64 (*.f64 a b))
320.0ms	(pow.f64 (cbrt.f64 (*.f64 a b)) 2)

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
349×	`log-prod_binary64`
136×	`expm1-udef_binary64`
136×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	187	22
2	1968	22

Stop Event

1×	node limit

Counts

3 → 88

Calls

3 calls:

40.0ms	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2) 3)
40.0ms	(pow.f64 (cbrt.f64 (*.f64 a b)) 2)
40.0ms	(cbrt.f64 (*.f64 a b))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-l_binary64`
560×	`associate-r_binary64`
384×	`unswap-sqr_binary64`
169×	`fma-neg_binary64`
133×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1320
1	127	1280
2	309	1136
3	1109	752
4	4806	752

Stop Event

1×	node limit

Counts

160 → 109

prune97.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	4	6	10
Picked	1	0	1
Done	0	2	2
Total	111	11	122

Error

0.0b

Counts

122 → 11

Alt Table

Status	Error	Program
	23.4b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (*.f64 a b)) 3)) b))
▶	0.9b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	20.7b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
	2.9b	(neg.f64 (.f64 (pow.f64 (.f64 b (pow.f64 (cbrt.f64 a) 2)) 2) (pow.f64 (cbrt.f64 a) 2)))
✓	16.3b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	18.4b	(neg.f64 (.f64 (pow.f64 (.f64 a (cbrt.f64 (.f64 b b))) 2) (cbrt.f64 (.f64 b b))))
	1.2b	(neg.f64 (pow.f64 (.f64 (cbrt.f64 a) (.f64 (cbrt.f64 b) (cbrt.f64 (*.f64 a b)))) 3))
	1.4b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 a b)) 2)) (pow.f64 (cbrt.f64 (*.f64 a b)) 4))))
✓	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	50.1b	(neg.f64 (.f64 a (pow.f64 (.f64 (sqrt.f64 a) b) 2)))
	4.3b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))

Compiler

Compiled 1740 to 1054 computations (39.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (*.f64 a b) 2)
✓	0.4b	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
✓	21.1b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series969.0ms (24.8%)

Counts

2 → 48

Calls

2 calls:

497.0ms	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
472.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

615×	`log1p-expm1-u_binary64`
615×	`expm1-log1p-u_binary64`
322×	`log-prod_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	184	16
2	1848	16

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

42.0ms	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
42.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

432×	`fma-neg_binary64`
399×	`fma-def_binary64`
345×	`exp-prod_binary64`
215×	`associate-l_binary64`
188×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	888
1	149	840
2	348	696
3	986	528
4	4025	504

Stop Event

1×	node limit

Counts

107 → 73

prune105.0ms (2.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	125	11	136

Error

0.0b

Counts

136 → 11

Alt Table

Status	Error	Program
	15.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)))) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 a b)) 2))))
✓	0.9b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	20.7b	(.f64 (.f64 a a) (*.f64 b (neg.f64 b)))
	2.9b	(neg.f64 (.f64 (pow.f64 (.f64 b (pow.f64 (cbrt.f64 a) 2)) 2) (pow.f64 (cbrt.f64 a) 2)))
✓	16.3b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	1.2b	(neg.f64 (pow.f64 (.f64 (cbrt.f64 a) (.f64 (cbrt.f64 b) (cbrt.f64 (*.f64 a b)))) 3))
	16.4b	(neg.f64 (*.f64 b (/.f64 b (pow.f64 a -2))))
✓	0.3b	(neg.f64 (pow.f64 (*.f64 a b) 2))
	15.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (.f64 a b))) (cbrt.f64 (*.f64 a b))))
	50.1b	(neg.f64 (.f64 a (pow.f64 (.f64 (sqrt.f64 a) b) 2)))
	4.3b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))

Compiler

Compiled 1892 to 1168 computations (38.3% saved)

regimes188.0ms (4.8%)

Accuracy

Total 0.3b remaining (83.1%)

Threshold costs 0.3b (83.1%)

Counts

47 → 1

Compiler

Compiled 3270 to 2244 computations (31.4% saved)

simplify2.0ms (0%)

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

end118.0ms (3%)

Remove: (sort a b)
Compiler: Compiled 177 to 122 computations (31.1% saved)

Details

analyze92.0ms (2.4%)

sample753.0ms (19.3%)

simplify11.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series17.0ms (0.4%)

rewrite33.0ms (0.9%)

simplify98.0ms (2.5%)

prune30.0ms (0.8%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite30.0ms (0.8%)

simplify68.0ms (1.7%)

prune49.0ms (1.3%)

localize6.0ms (0.2%)

series1.0s (26.5%)

rewrite42.0ms (1.1%)

simplify50.0ms (1.3%)

prune97.0ms (2.5%)

localize7.0ms (0.2%)

series969.0ms (24.8%)

rewrite44.0ms (1.1%)

simplify41.0ms (1.1%)

prune105.0ms (2.7%)

regimes188.0ms (4.8%)

simplify2.0ms (0%)

end118.0ms (3%)

Profiling