Details

analyze925.0ms (11.4%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.5s (30.6%)

Results

775.0ms	5364×	body	128	valid
657.0ms	1169×	body	2048	valid
323.0ms	775×	body	1024	valid
253.0ms	414×	body	4096	valid
135.0ms	1010×	body	128	invalid
110.0ms	341×	body	512	valid
50.0ms	193×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify155.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

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

32.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series172.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

75.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
46.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
40.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite249.0ms (3.1%)

Algorithm

4×	egg-rewrite

Rules

50×	`egg`
49×	`egg`
46×	`egg`
23×	`egg`

Counts

4 → 168

Calls

4 calls:

89.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
63.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
48.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
44.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	178	13
2	1913	13
3	5067	13
0	10	16
1	209	16
2	2469	16
3	4778	15
4	4940	15
0	11	19
1	235	19
2	2944	19
3	5021	19
0	8	11
1	159	11
2	1723	11
3	5314	11

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
480×	`associate-/l*_binary64`
434×	`associate-/r*_binary64`
344×	`fma-def_binary64`
209×	`fma-neg_binary64`

Counts

264 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	2081
1	351	1997
2	1169	1913
3	4896	1913
4	4993	1913

prune170.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	229	9	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	230	9	239

Error

4.5b

Counts

239 → 9

Alt Table

Status	Error	Program
	34.8b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	46.8b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (*.f64 b b)))) a))
	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.9b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
	33.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))

Compiler

Compiled 5835 to 3551 computations (39.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 c -4) a (.f64 b b))
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b)))) a)
✓	1.7b	(+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b))))
✓	21.2b	(sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b)))

series165.0ms (2%)

Counts

4 → 96

Calls

4 calls:

68.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b)))) a)
47.0ms	(+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b))))
40.0ms	(sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b)))
10.0ms	(fma.f64 (.f64 c -4) a (.f64 b b))

rewrite249.0ms (3.1%)

Algorithm

4×	egg-rewrite

Rules

50×	`egg`
49×	`egg`
46×	`egg`
23×	`egg`

Counts

4 → 168

Calls

4 calls:

90.0ms	(+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b))))
62.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b)))) a)
49.0ms	(sqrt.f64 (fma.f64 (.f64 c -4) a (.f64 b b)))
45.0ms	(fma.f64 (.f64 c -4) a (.f64 b b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	178	13
2	1913	13
3	5067	13
0	10	16
1	209	16
2	2469	16
3	4778	15
4	4937	15
0	11	19
1	235	19
2	2944	19
3	5020	19
0	8	11
1	159	11
2	1723	11
3	5314	11

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
480×	`associate-/l*_binary64`
434×	`associate-/r*_binary64`
344×	`fma-def_binary64`
209×	`fma-neg_binary64`

Counts

264 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	2081
1	351	1997
2	1169	1913
3	4896	1913
4	4993	1913

prune161.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	238	9	247

Error

4.5b

Counts

247 → 9

Alt Table

Status	Error	Program
	34.8b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	46.8b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (*.f64 b b)))) a))
▶	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.9b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
	33.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))

Compiler

Compiled 5817 to 3538 computations (39.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series69.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

68.0ms

(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

rewrite75.0ms (0.9%)

Algorithm

1×	egg-rewrite

Rules

67× egg

Counts

1 → 67

Calls

1 calls:

73.0ms

(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	271	19
2	3181	19
3	5232	19

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

751×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
285×	`fma-neg_binary64`
236×	`associate-r_binary64`

Counts

87 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	567
1	195	555
2	629	529
3	3169	529
4	5154	529

prune180.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	254	2	256
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	256	9	265

Error

4.5b

Counts

265 → 9

Alt Table

Status	Error	Program
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (*.f64 b b)))) a))
✓	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	44.9b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	47.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
▶	33.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	34.8b	(.f64 -1/2 (.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (/.f64 1 a)))

Compiler

Compiled 6638 to 4150 computations (37.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	1.7b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series276.0ms (3.4%)

Counts

2 → 40

Calls

2 calls:

208.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
68.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

rewrite139.0ms (1.7%)

Algorithm

2×	egg-rewrite

Rules

61×	`egg`
45×	`egg`

Counts

2 → 106

Calls

2 calls:

73.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
63.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	276	19
2	3353	19
3	5034	19
0	11	19
1	235	19
2	2938	19
3	5015	19

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
520×	`associate-/l*_binary64`
485×	`associate-/r*_binary64`
256×	`fma-def_binary64`
233×	`fma-neg_binary64`

Counts

146 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1240
1	318	1192
2	1113	1138
3	4905	1138
4	5047	1138

prune188.0ms (2.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	259	10	269

Error

4.3b

Counts

269 → 10

Alt Table

Status	Error	Program
	44.9b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	38.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
✓	32.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c -4) a (*.f64 b b)))) a))
✓	33.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	50.6b	(.f64 -1/2 (exp.f64 (-.f64 (log.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (log.f64 a))))
✓	33.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	34.8b	(.f64 -1/2 (.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (/.f64 1 a)))

Compiler

Compiled 6785 to 4253 computations (37.3% saved)

regimes2.0s (24.1%)

Accuracy

Total 5.3b remaining (49.2%)

Threshold costs 0b (0%)

Counts

141 → 3

Compiler

Compiled 12300 to 8642 computations (29.7% saved)

bsearch48.0ms (0.6%)

Steps

Iters	Range		Point
6	3.8657611513446867e+90	2.928767619032365e+91	2.818024375880192e+91
5	-1.1401732337828577e-138	-2.8577058786826562e-139	-1.1192253259106201e-138

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	63
1	43	63
2	49	63
3	53	63
4	56	63
5	57	63
6	56	63

end136.0ms (1.7%)

Compiler: Compiled 275 to 191 computations (30.5% saved)

Details

analyze925.0ms (11.4%)

sample2.5s (30.6%)

simplify155.0ms (1.9%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series172.0ms (2.1%)

rewrite249.0ms (3.1%)

simplify81.0ms (1%)

prune170.0ms (2.1%)

localize9.0ms (0.1%)

series165.0ms (2%)

rewrite249.0ms (3.1%)

simplify82.0ms (1%)

prune161.0ms (2%)

localize11.0ms (0.1%)

series69.0ms (0.8%)

rewrite75.0ms (0.9%)

simplify52.0ms (0.6%)

prune180.0ms (2.2%)

localize12.0ms (0.2%)

series276.0ms (3.4%)

rewrite139.0ms (1.7%)

simplify69.0ms (0.9%)

prune188.0ms (2.3%)

regimes2.0s (24.1%)

bsearch48.0ms (0.6%)

simplify4.0ms (0.1%)

end136.0ms (1.7%)

Profiling