Details

analyze103.0ms (3.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 20 to 11 computations (45% saved)

sample29.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	1×	pre	128	false

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify71.0ms (2.4%)

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

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

13.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.8b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
▶	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 79 to 45 computations (43% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	13.4b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
10×	`fabs-mul_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

11.0ms	(-.f64 (.f64 a a) (.f64 b b))
6.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
5.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series82.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

42.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
21.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
19.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify130.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
330×	`associate-l_binary64`
306×	`associate-/l*_binary64`
296×	`fma-neg_binary64`
282×	`associate-r_binary64`

Counts

147 → 266

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2391
1	285	2222
2	879	2113
3	3871	2101
4	4888	2101
5	4981	2101

prune89.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	263	3	266
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	264	4	268

Error

Counts

268 → 4

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
▶	0.0b	(*.f64 1 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))))
	0.1b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) a))) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a))))
✓	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 2509 to 718 computations (71.4% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`sqrt-prod_binary64`
7×	`add-sqr-sqrt_binary64`
4×	`fabs-mul_binary64`
3×	`rem-sqrt-square_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

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

series16.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

16.0ms

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

simplify119.0ms (4%)

Algorithm

1×	egg-herbie

Rules

623×	`div-sub_binary64`
521×	`fma-def_binary64`
500×	`unsub-neg_binary64`
476×	`distribute-neg-in_binary64`
362×	`unswap-sqr_binary64`

Counts

21 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	397
1	44	370
2	56	370
3	72	370
4	105	370
5	160	370
6	263	370
7	535	370
8	1105	370
9	2806	370
10	3741	370
11	4491	370
12	4947	370
13	4784	370

prune26.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	27	4	31

Error

Counts

31 → 4

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
✓	0.0b	(*.f64 1 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))))
	0.1b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) a))) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a))))
✓	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 556 to 305 computations (45.1% saved)

localize9.0ms (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)
✓	0.0b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 155

Calls

4 calls:

15.0ms	(*.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)
1.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))

series95.0ms (3.2%)

Counts

4 → 96

Calls

4 calls:

43.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
21.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
15.0ms	(/.f64 (-.f64 a b) a)
15.0ms	(/.f64 (+.f64 a b) a)

simplify181.0ms (6%)

Algorithm

1×	egg-herbie

Rules

581×	`times-frac_binary64`
553×	`distribute-rgt-in_binary64`
530×	`distribute-lft-in_binary64`
264×	`fma-def_binary64`
146×	`associate-*l/_binary64`

Counts

251 → 423

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	3891
1	540	3637
2	1757	3631
3	4659	3617
4	4992	3617
5	4904	3617

prune175.0ms (5.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	423	4	427

Error

Counts

427 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
✓	0.0b	(*.f64 1 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))))
▶	0.1b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) a))) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a))))
✓	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 5104 to 1342 computations (73.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

227×	`add-sqr-sqrt_binary64`
129×	`sqrt-prod_binary64`
100×	`fabs-mul_binary64`
91×	`times-frac_binary64`
55×	`rem-sqrt-square_binary64`

Counts

2 → 172

Calls

2 calls:

25.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) a))) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a))))
7.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a)))

series54.0ms (1.8%)

Counts

2 → 28

Calls

2 calls:

39.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) a))) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a))))
14.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a)))

simplify311.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

707×	`times-frac_binary64`
637×	`fma-def_binary64`
514×	`associate-/l*_binary64`
421×	`fma-neg_binary64`
410×	`associate-*l/_binary64`

Counts

200 → 328

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	275	5778
1	495	5676
2	940	5610
3	1406	5603
4	3618	5562
5	3735	5562
6	4346	5562
7	4958	5562
8	4886	5562

prune271.0ms (9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	505	0	505
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	505	4	509

Error

Counts

509 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
✓	0.0b	(*.f64 1 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))))
✓	0.1b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) a))) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) a))))
✓	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 8494 to 1492 computations (82.4% saved)

regimes205.0ms (6.8%)

Accuracy

Total 0.0b remaining (72.8%)

Threshold costs 0.0b (72.8%)

Compiler

Compiled 3774 to 2453 computations (35% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	8	15

end0.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample900.0ms (29.9%)

Algorithm

1×

intervals

Results

369.0ms	8000×	body	128	valid
175.0ms	8000×	pre	128	true
3.0ms	127×	pre	128	false

Compiler

Compiled 95 to 57 computations (40% saved)

Details

analyze103.0ms (3.4%)

sample29.0ms (1%)

simplify71.0ms (2.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite26.0ms (0.9%)

series82.0ms (2.7%)

simplify130.0ms (4.3%)

prune89.0ms (3%)

localize7.0ms (0.2%)

rewrite3.0ms (0.1%)

series16.0ms (0.5%)

simplify119.0ms (4%)

prune26.0ms (0.8%)

localize9.0ms (0.3%)

rewrite36.0ms (1.2%)

series95.0ms (3.2%)

simplify181.0ms (6%)

prune175.0ms (5.8%)

localize10.0ms (0.3%)

rewrite47.0ms (1.6%)

series54.0ms (1.8%)

simplify311.0ms (10.3%)

prune271.0ms (9%)

regimes205.0ms (6.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample900.0ms (29.9%)

Profiling