Details

analyze384.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.2s (64.6%)

Results

1.5s	2574×	body	1024	valid
711.0ms	1195×	body	2048	valid
485.0ms	1278×	body	512	valid
290.0ms	2484×	body	128	valid
147.0ms	681×	body	256	valid
32.0ms	44×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

45.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.4b	(+.f64 x (hypot.f64 1 x))
✓	3.3b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite96.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

85× egg-rr

Counts

3 → 85

Calls

2 calls:

95.0ms	((log.f64 (+.f64 x (hypot.f64 1 x))) (+.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	120	20
2	1436	20
3	4831	20
4	4804	20
5	4976	20
0	0	0
1	0	0

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-neg_binary64`
722×	`times-frac_binary64`
447×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
340×	`sub-neg_binary64`

Counts

121 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	569
1	305	549
2	805	537
3	2329	537
4	4446	537
5	5590	537

prune67.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Error

0.0b

Counts

150 → 3

Alt Table

Status	Error	Program
	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
▶	33.7b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 1980 to 1478 computations (25.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	0.0b	(*.f64 5/112 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	26.6b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

series18.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
5.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
4.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
4.0ms	(*.f64 5/112 (pow.f64 x 7))

rewrite67.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

110× egg-rr

Counts

4 → 110

Calls

2 calls:

64.0ms

((-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) (*.f64 5/112 (pow.f64 x 7)) (fma.f64 3/40 (pow.f64 x 5) x))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	332	53
2	3556	53
3	4939	53
0	0	0
1	0	0

simplify171.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

921×	`distribute-rgt-neg-in_binary64`
534×	`sqr-pow_binary64`
489×	`fma-neg_binary64`
428×	`sub-neg_binary64`
396×	`cancel-sign-sub-inv_binary64`

Counts

146 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	426
1	70	422
2	164	414
3	422	408
4	1180	408
5	1924	408
6	2643	408
7	3577	408
8	3489	408
9	3665	408
10	3867	408
11	4057	408
12	3819	408
13	4825	408
14	4889	408

prune102.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	4	131

Error

Counts

131 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	58.2b	(pow.f64 (pow.f64 (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) 3) 1/3)
▶	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	33.7b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

Compiler

Compiled 3522 to 2813 computations (20.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
✓	0.1b	(/.f64 1/8 (pow.f64 x 3))
✓	11.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series11.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
3.0ms	(/.f64 1/8 (pow.f64 x 3))
3.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))

rewrite61.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

104× egg-rr

Counts

3 → 104

Calls

2 calls:

60.0ms	((log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))) (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	230	31
2	2886	31
3	4884	31
0	0	0
1	0	0

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-neg_binary64`
732×	`fma-def_binary64`
685×	`times-frac_binary64`
524×	`cancel-sign-sub-inv_binary64`
387×	`associate-l_binary64`

Counts

128 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	410
1	180	402
2	497	400
3	1626	396
4	4148	396
5	5672	396

prune63.0ms (1.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	58.2b	(pow.f64 (pow.f64 (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) 3) 1/3)
✓	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	33.7b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

Compiler

Compiled 2214 to 1760 computations (20.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 5/112 (pow.f64 x 7))
	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
	26.6b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
✓	34.2b	(pow.f64 (pow.f64 (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) 3) 1/3)

series8.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(pow.f64 (pow.f64 (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) 3) 1/3)

rewrite60.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

56× egg-rr

Counts

1 → 56

Calls

2 calls:

58.0ms	((pow.f64 (pow.f64 (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) 3) 1/3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	381	24
2	3956	24
3	4816	24
0	0	0
1	0	0

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
647×	`associate-/l*_binary64`
585×	`cancel-sign-sub-inv_binary64`
574×	`fma-neg_binary64`
166×	`distribute-rgt-neg-in_binary64`

Counts

68 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	546
1	193	522
2	492	400
3	1650	303
4	4705	301
5	4961	301
6	4901	301

prune166.0ms (3.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	182	4	186

Error

Counts

186 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	58.2b	(pow.f64 (pow.f64 (-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))) 3) 1/3)
✓	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	33.7b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

Compiler

Compiled 6107 to 4992 computations (18.3% saved)

regimes105.0ms (2.1%)

Accuracy

Total 0.1b remaining (76%)

Threshold costs 0.1b (76%)

Counts

25 → 3

Compiler

Compiled 879 to 682 computations (22.4% saved)

bsearch41.0ms (0.8%)

Steps

Iters	Range		Point
10	0.01710817362014471	4615241499492.261	0.02259612619328486
10	-118685.5196701979	-3.1843737634226373e-14	-1.1533316581136956

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	56
1	35	56
2	34	56

end96.0ms (2%)

Compiler: Compiled 138 to 106 computations (23.2% saved)

Details

analyze384.0ms (7.8%)

sample3.2s (64.6%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite96.0ms (2%)

simplify57.0ms (1.2%)

prune67.0ms (1.4%)

localize10.0ms (0.2%)

series18.0ms (0.4%)

rewrite67.0ms (1.4%)

simplify171.0ms (3.5%)

prune102.0ms (2.1%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite61.0ms (1.2%)

simplify51.0ms (1%)

prune63.0ms (1.3%)

localize15.0ms (0.3%)

series8.0ms (0.2%)

rewrite60.0ms (1.2%)

simplify64.0ms (1.3%)

prune166.0ms (3.4%)

regimes105.0ms (2.1%)

bsearch41.0ms (0.8%)

simplify2.0ms (0%)

end96.0ms (2%)

Profiling