Details

analyze644.0ms (5.3%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.8s (22.8%)

Results

928.0ms	5362×	body	128	valid
596.0ms	1236×	body	2048	valid
317.0ms	714×	body	1024	valid
235.0ms	407×	body	4096	valid
132.0ms	164×	body	256	valid
130.0ms	1082×	body	128	invalid
115.0ms	373×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
205×	`fma-def_binary64`
183×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series191.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

102.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
54.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
27.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
60×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 176

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify194.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
181×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
135×	`associate-r_binary64`

Counts

272 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	8791
1	779	6792
2	2682	5750
3	4584	5750
4	4974	5750

prune259.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	282	10	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	283	10	293

Error

6.6b

Counts

293 → 10

Alt Table

Status	Error	Program
	45.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	44.8b	(/.f64 (*.f64 -2 b_2) a)
	31.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	37.6b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	57.3b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
▶	31.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
	32.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 a)))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))
	36.6b	(/.f64 (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)

Compiler

Compiled 9072 to 1994 computations (78% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
	0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	4.7b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
	21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series92.0ms (0.8%)

Counts

2 → 40

Calls

2 calls:

49.0ms	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
43.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)

rewrite378.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

1357×	`times-frac_binary64`
955×	`add-sqr-sqrt_binary64`
950×	`*-un-lft-identity_binary64`
936×	`add-cube-cbrt_binary64`
748×	`prod-diff_binary64`

Counts

2 → 877

Calls

2 calls:

48.0ms	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
5.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)

simplify1.4s (11.1%)

Algorithm

1×	egg-herbie

Rules

473×	`unsub-neg_binary64`
420×	`fma-udef_binary64`
363×	`fma-neg_binary64`
338×	`associate-+r-_binary64`
275×	`sub-neg_binary64`

Counts

917 → 893

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	741	69731
1	1634	45707
2	3415	32198
3	4475	32198
4	4823	32198
5	4815	32198

prune520.0ms (4.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	970	4	974
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	973	11	984

Error

6.6b

Counts

984 → 11

Alt Table

Status	Error	Program
	37.6b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
▶	31.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a))
	57.3b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	36.6b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	43.5b	(-.f64 (/.f64 (neg.f64 b_2) a) (expm1.f64 (log1p.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))
	45.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	44.8b	(/.f64 (*.f64 -2 b_2) a)
	31.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	32.0b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (/.f64 a (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))

Compiler

Compiled 63152 to 7916 computations (87.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a)
✓	0.5b	(fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))
✓	4.7b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a))
✓	21.6b	(sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a))))

series130.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

53.0ms	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a))
41.0ms	(/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a)
27.0ms	(sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a))))
8.0ms	(fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))

rewrite323.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1357×	`times-frac_binary64`
959×	`add-sqr-sqrt_binary64`
953×	`*-un-lft-identity_binary64`
939×	`add-cube-cbrt_binary64`
748×	`prod-diff_binary64`

Counts

4 → 900

Calls

4 calls:

47.0ms	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a)
1.0ms	(sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a))))
0.0ms	(fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))

simplify1.4s (11.5%)

Algorithm

1×	egg-herbie

Rules

491×	`unsub-neg_binary64`
421×	`fma-udef_binary64`
400×	`sub-neg_binary64`
400×	`fma-neg_binary64`
341×	`associate-+r-_binary64`

Counts

996 → 955

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	770	70922
1	1703	46864
2	3725	33340
3	4428	33340
4	4904	33340
5	4993	33340
6	4848	33340

prune459.0ms (3.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	955	0	955
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	955	11	966

Error

6.6b

Counts

966 → 11

Alt Table

Status	Error	Program
	37.6b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
✓	31.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a))
	57.3b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	36.6b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	43.5b	(-.f64 (/.f64 (neg.f64 b_2) a) (expm1.f64 (log1p.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))
	45.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	44.8b	(/.f64 (*.f64 -2 b_2) a)
▶	31.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	32.0b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (/.f64 a (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))

Compiler

Compiled 62611 to 7763 computations (87.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series51.0ms (0.4%)

Counts

1 → 20

Calls

1 calls:

51.0ms

(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 46

Calls

1 calls:

12.0ms

(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
400×	`fma-neg_binary64`
392×	`associate-/l*_binary64`
309×	`fma-def_binary64`
212×	`distribute-rgt-in_binary64`

Counts

66 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1869
1	398	1694
2	1327	1613
3	4987	1613
4	5215	1613

prune166.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	296	3	299
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	300	10	310

Error

6.6b

Counts

310 → 10

Alt Table

Status	Error	Program
	57.3b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	36.6b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	43.5b	(-.f64 (/.f64 (neg.f64 b_2) a) (expm1.f64 (log1p.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))
	45.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
✓	31.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (sqrt.f64 (fma.f64 b_2 b_2 (neg.f64 (*.f64 c a)))) a))
	44.8b	(.f64 (.f64 b_2 -2) (/.f64 1 a))
	34.0b	(/.f64 (/.f64 (.f64 c a) a) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
	41.0b	(/.f64 (.f64 c a) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

Compiler

Compiled 9386 to 2527 computations (73.1% saved)

regimes2.7s (21.8%)

Accuracy

Total 4.0b remaining (41.2%)

Threshold costs 0b (0%)

Counts

152 → 5

Compiler

Compiled 16551 to 8593 computations (48.1% saved)

bsearch168.0ms (1.4%)

Steps

Iters	Range		Point
10	8.706791209674724e+40	1.0718853353162449e+52	1.0611311445557777e+52
2	-1.7063633921354645e-73	-1.4791265736148994e-73	-1.677958789820394e-73
10	-1.5814650309630123e-33	-4.0696904308218766e-45	-2.583305902750818e-39
10	-1.539049726447568e+63	-6.3647163022481495e+50	-3.566979873129798e+56

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	101
1	59	99
2	78	99
3	94	99
4	102	99
5	104	99
6	104	99

end146.0ms (1.2%)

Compiler: Compiled 292 to 178 computations (39% saved)

Details

analyze644.0ms (5.3%)

sample2.8s (22.8%)

simplify82.0ms (0.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series191.0ms (1.6%)

rewrite45.0ms (0.4%)

simplify194.0ms (1.6%)

prune259.0ms (2.1%)

localize9.0ms (0.1%)

series92.0ms (0.8%)

rewrite378.0ms (3.1%)

simplify1.4s (11.1%)

prune520.0ms (4.3%)

localize12.0ms (0.1%)

series130.0ms (1.1%)

rewrite323.0ms (2.6%)

simplify1.4s (11.5%)

prune459.0ms (3.8%)

localize12.0ms (0.1%)

series51.0ms (0.4%)

rewrite16.0ms (0.1%)

simplify90.0ms (0.7%)

prune166.0ms (1.4%)

regimes2.7s (21.8%)

bsearch168.0ms (1.4%)

simplify5.0ms (0%)

end146.0ms (1.2%)

Profiling