Details

analyze34.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.1s (40.3%)

Results

945.0ms	8256×	body	128	valid
43.0ms	360×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify46.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune5.0ms (0.2%)

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

14.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.5b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	14.5b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 79 to 45 computations (43% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	14.5b	(/.f64 b (*.f64 a a))

series34.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(/.f64 b (*.f64 a a))
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite48.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
142×	`log1p-udef_binary64`
90×	`add-sqr-sqrt_binary64`
84×	`add-cbrt-cube_binary64`

Counts

2 → 59

Calls

2 calls:

47.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
47.0ms	(/.f64 b (*.f64 a a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	182	20
2	1989	20
3	4975	20
0	0	0
1	0	0

simplify113.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1214×	`fma-def_binary64`
706×	`associate-/r/_binary64`
598×	`div-sub_binary64`
525×	`fma-neg_binary64`
434×	`unswap-sqr_binary64`

Counts

107 → 62

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	528
1	17	528
2	29	528
3	54	528
4	120	528
5	336	528
6	1160	528
7	1957	528
8	2364	528
9	2778	528
10	3554	528
11	4092	528
12	4278	528
13	4997	528

prune32.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Error

0.0b

Counts

64 → 2

Alt Table

Status	Error	Program
	14.5b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))

Compiler

Compiled 904 to 477 computations (47.2% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
✓	0.3b	(/.f64 (sqrt.f64 b) a)
✓	0.5b	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)

series35.0ms (1.3%)

Counts

3 → 48

Calls

3 calls:

14.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
8.0ms	(/.f64 (sqrt.f64 b) a)

rewrite67.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

855×	`log1p-expm1-u_binary64`
855×	`expm1-log1p-u_binary64`
104×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`
98×	`add-log-exp_binary64`

Counts

3 → 97

Calls

3 calls:

66.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
66.0ms	(/.f64 (sqrt.f64 b) a)
66.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	221	26
2	2217	26
3	5184	26
0	0	0
1	0	0

simplify92.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

618×	`unswap-sqr_binary64`
568×	`fma-def_binary64`
412×	`associate-/l*_binary64`
361×	`fma-neg_binary64`
317×	`*-commutative_binary64`

Counts

145 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	672
1	29	564
2	57	516
3	170	516
4	700	516
5	1694	516
6	2108	516
7	2766	516
8	3807	516
9	4825	516
10	4942	516

prune52.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	100	2	102

Error

0.0b

Counts

102 → 2

Alt Table

Status	Error	Program
▶	14.5b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))

Compiler

Compiled 1522 to 789 computations (48.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	14.1b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series40.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
20.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

rewrite116.0ms (4.5%)

Algorithm

2×	batch-egg-rewrite

Rules

881×	`prod-diff_binary64`
644×	`fma-udef_binary64`
290×	`fma-neg_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`

Counts

2 → 79

Calls

2 calls:

115.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
115.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	212	28
2	2703	28
3	4707	28
4	4641	27
5	5152	27
0	0	0
1	0	0

simplify57.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

722×	`associate-/r*_binary64`
695×	`associate-/l/_binary64`
512×	`associate-/r/_binary64`
495×	`fma-def_binary64`
443×	`associate-*l/_binary64`

Counts

127 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	753
1	36	681
2	79	633
3	250	633
4	1040	633
5	4492	633
6	5129	633

prune52.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	83	4	87

Error

0.0b

Counts

87 → 4

Alt Table

Status	Error	Program
✓	14.5b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
	1.2b	(sqrt.f64 (fabs.f64 1))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))

Compiler

Compiled 1436 to 565 computations (60.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 a b) a)
✓	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
✓	0.0b	(/.f64 (-.f64 a b) a)
✓	0.1b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))

series43.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
13.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
5.0ms	(/.f64 (-.f64 a b) a)
4.0ms	(/.f64 (+.f64 a b) a)

rewrite77.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

588×	`prod-diff_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
161×	`egg-rr`
121×	`add-sqr-sqrt_binary64`

Counts

4 → 161

Calls

4 calls:

75.0ms	(/.f64 (+.f64 a b) a)
75.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
75.0ms	(/.f64 (-.f64 a b) a)
74.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	50
1	236	45
2	3311	45
3	5056	45
0	0	0
1	0	0

simplify60.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

468×	`cancel-sign-sub-inv_binary64`
378×	`div-sub_binary64`
321×	`fma-neg_binary64`
291×	`fma-def_binary64`
261×	`fabs-div_binary64`

Counts

257 → 173

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	1041
1	74	1041
2	199	1041
3	639	1041
4	2781	1041
5	5183	1041

prune126.0ms (4.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	0	1
Picked	1	0	1
Done	2	0	2
Total	175	2	177

Error

Counts

177 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))))
	0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (*.f64 (/.f64 a (+.f64 a b)) (/.f64 a (-.f64 a b))))))

Compiler

Compiled 2834 to 898 computations (68.3% saved)

regimes345.0ms (13.2%)

Accuracy

Total 0.0b remaining (60%)

Threshold costs 0.0b (60%)

Counts

66 → 1

Compiler

Compiled 7826 to 5031 computations (35.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	16	24
2	21	24
3	23	24
4	24	24
5	24	24

end50.0ms (1.9%)

Compiler: Compiled 68 to 44 computations (35.3% saved)

Details

analyze34.0ms (1.3%)

sample1.1s (40.3%)

simplify46.0ms (1.8%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

series34.0ms (1.3%)

rewrite48.0ms (1.8%)

simplify113.0ms (4.3%)

prune32.0ms (1.2%)

localize9.0ms (0.3%)

series35.0ms (1.3%)

rewrite67.0ms (2.6%)

simplify92.0ms (3.5%)

prune52.0ms (2%)

localize7.0ms (0.3%)

series40.0ms (1.5%)

rewrite116.0ms (4.5%)

simplify57.0ms (2.2%)

prune52.0ms (2%)

localize8.0ms (0.3%)

series43.0ms (1.7%)

rewrite77.0ms (3%)

simplify60.0ms (2.3%)

prune126.0ms (4.8%)

regimes345.0ms (13.2%)

simplify3.0ms (0.1%)

end50.0ms (1.9%)

Profiling