Details

analyze368.0ms (5.3%)

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)

sample3.5s (50.4%)

Results

1.7s	2574×	body	1024	valid
753.0ms	1195×	body	2048	valid
471.0ms	1278×	body	512	valid
280.0ms	2484×	body	128	valid
178.0ms	681×	body	256	valid
30.0ms	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%)

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)

localize4.0ms (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 (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(hypot.f64 1 x)

rewrite280.0ms (4%)

Algorithm

3×	egg-rewrite

Rules

49×	`egg`
38×	`egg`
21×	`egg`

Counts

3 → 108

Calls

3 calls:

154.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
87.0ms	(+.f64 x (hypot.f64 1 x))
37.0ms	(hypot.f64 1 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	120	9
2	1436	9
3	4831	9
4	4804	9
5	4976	9
0	5	7
1	104	7
2	1265	7
3	4933	7
4	6724	7
0	4	4
1	73	4
2	722	4
3	5008	4

simplify72.0ms (1%)

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

144 → 172

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

prune94.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	3	173

Error

0.0b

Counts

173 → 3

Alt Table

Status	Error	Program
	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 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 2305 to 1735 computations (24.7% saved)

localize10.0ms (0.1%)

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))))

series19.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

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

rewrite286.0ms (4.1%)

Algorithm

4×	egg-rewrite

Rules

55×	`egg`
48×	`egg`
43×	`egg`
23×	`egg`

Counts

4 → 169

Calls

4 calls:

81.0ms	(*.f64 5/112 (pow.f64 x 7))
76.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
72.0ms	(-.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))))
52.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	332	24
2	3556	24
3	4939	24
0	10	14
1	213	14
2	2131	14
3	5001	14
0	6	7
1	127	7
2	1309	7
3	4944	7
4	6454	7
0	6	8
1	128	8
2	1329	8
3	4928	8
4	4952	8

simplify189.0ms (2.7%)

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

205 → 186

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

prune165.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
	47.4b	(-.f64 (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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))))) (/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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))))))
▶	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 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 5115 to 4080 computations (20.2% saved)

localize7.0ms (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)))

series12.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
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))

rewrite168.0ms (2.4%)

Algorithm

3×	egg-rewrite

Rules

60×	`egg`
46×	`egg`
25×	`egg`

Counts

3 → 131

Calls

3 calls:

62.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
61.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
42.0ms	(/.f64 1/8 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	230	13
2	2886	13
3	4884	13
0	6	7
1	132	7
2	1417	7
3	4929	7
0	9	13
1	214	11
2	2715	11
3	4924	11

simplify61.0ms (0.9%)

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

155 → 156

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

prune83.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	156	4	160

Error

Counts

160 → 4

Alt Table

Status	Error	Program
▶	47.4b	(-.f64 (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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))))) (/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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))))))
✓	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 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 2670 to 2136 computations (20% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) 2)
✓	20.8b	(-.f64 (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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))))) (/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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))))))
✓	30.4b	(/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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)))))
✓	43.2b	(/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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)))))

series22.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(-.f64 (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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))))) (/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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))))))
5.0ms	(pow.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) 2)
5.0ms	(/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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)))))

rewrite329.0ms (4.8%)

Algorithm

4×	egg-rewrite

Rules

51×	`egg`
47×	`egg`
45×	`egg`
39×	`egg`

Counts

4 → 182

Calls

4 calls:

97.0ms	(-.f64 (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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))))) (/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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))))))
82.0ms	(/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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)))))
81.0ms	(/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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)))))
62.0ms	(pow.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	399	37
2	4298	37
3	5536	37
0	18	43
1	399	43
2	4296	43
3	5538	43
0	21	56
1	480	56
2	4656	56
3	5371	56
0	12	17
1	255	17
2	2420	17
3	5654	17

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-l_binary64`
493×	`fma-neg_binary64`
480×	`cancel-sign-sub-inv_binary64`
464×	`sub-neg_binary64`
457×	`associate-r_binary64`

Counts

230 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	789
1	255	757
2	665	735
3	1735	735
4	4005	735
5	4658	735
6	4885	735
7	4911	735

prune414.0ms (6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	230	4	234

Error

Counts

234 → 4

Alt Table

Status	Error	Program
✓	47.4b	(-.f64 (/.f64 (pow.f64 (fma.f64 3/40 (pow.f64 x 5) x) 2) (+.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))))) (/.f64 (pow.f64 (fma.f64 1/6 (pow.f64 x 3) (.f64 5/112 (pow.f64 x 7))) 2) (+.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))))))
✓	46.4b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 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 15820 to 12648 computations (20.1% saved)

regimes530.0ms (7.7%)

Accuracy

Total 0.2b remaining (88.7%)

Threshold costs 0.2b (88.7%)

Counts

39 → 3

Compiler

Compiled 2880 to 2272 computations (21.1% saved)

bsearch43.0ms (0.6%)

Steps

Iters	Range		Point
10	0.01710817362014471	4615241499492.261	1.2999681543863966
10	-118685.5196701979	-3.1843737634226373e-14	-1.1533316581136956

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	31	57
1	36	57
2	41	57
3	43	57
4	44	57
5	44	57

end121.0ms (1.7%)

Compiler: Compiled 174 to 136 computations (21.8% saved)

Details

analyze368.0ms (5.3%)

sample3.5s (50.4%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize4.0ms (0.1%)

series9.0ms (0.1%)

rewrite280.0ms (4%)

simplify72.0ms (1%)

prune94.0ms (1.4%)

localize10.0ms (0.1%)

series19.0ms (0.3%)

rewrite286.0ms (4.1%)

simplify189.0ms (2.7%)

prune165.0ms (2.4%)

localize7.0ms (0.1%)

series12.0ms (0.2%)

rewrite168.0ms (2.4%)

simplify61.0ms (0.9%)

prune83.0ms (1.2%)

localize20.0ms (0.3%)

series22.0ms (0.3%)

rewrite329.0ms (4.8%)

simplify113.0ms (1.6%)

prune414.0ms (6%)

regimes530.0ms (7.7%)

bsearch43.0ms (0.6%)

simplify3.0ms (0%)

end121.0ms (1.7%)

Profiling