Details

analyze279.0ms (3.4%)

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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
40.6%	54.6%	4.8%	7
48.4%	46%	5.6%	8
53.8%	37.8%	8.3%	9
56.2%	32.6%	11.3%	10
60.8%	26%	13.1%	11
63.8%	21%	15.2%	12
65.1%	17.8%	17%	13
67.7%	13.9%	18.4%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.2s (26.4%)

Results

561.0ms	5626×	body	128	valid
403.0ms	1043×	body	2048	valid
214.0ms	679×	body	1024	valid
187.0ms	391×	body	4096	valid
114.0ms	717×	body	128	invalid
80.0ms	340×	body	512	valid
29.0ms	177×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify84.0ms (1%)

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

30.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.6b	(/.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)

localize10.0ms (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)
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.1b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series193.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
60.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite105.0ms (1.3%)

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))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify191.0ms (2.3%)

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

prune279.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	282	10	292
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	11	293

Error

4.9b

Counts

293 → 11

Alt Table

Status	Error	Program
	41.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	41.8b	(/.f64 (*.f64 -2 b_2) a)
▶	31.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	31.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a))) (cbrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
✓	30.6b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	49.6b	(.f64 (+.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (neg.f64 b_2))) (/.f64 (-.f64 (sqrt.f64 (neg.f64 b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	33.2b	(/.f64 (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)
	31.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (cbrt.f64 a)))
	33.8b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	54.2b	(log.f64 (exp.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 9134 to 2022 computations (77.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
✓	0.2b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	11.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.1s (13%)

Counts

4 → 42

Calls

4 calls:

527.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
326.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
195.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
18.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`*-un-lft-identity_binary64`
162×	`times-frac_binary64`
139×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
34×	`distribute-lft-out--_binary64`

Counts

4 → 244

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
6.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
5.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify255.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
401×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
186×	`sub-neg_binary64`
154×	`distribute-frac-neg_binary64`

Counts

286 → 331

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	9712
1	794	8164
2	2705	7612
3	4798	7608
4	4906	7608

prune226.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	327	4	331
Fresh	6	3	9
Picked	1	0	1
Done	0	1	1
Total	334	8	342

Error

0.1b

Counts

342 → 8

Alt Table

Status	Error	Program
✓	30.6b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	47.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	41.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	46.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
	42.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
▶	31.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (cbrt.f64 a)))
	45.4b	(.f64 (/.f64 1 (/.f64 a (-.f64 (.f64 (neg.f64 b_2) (neg.f64 b_2)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))) (/.f64 1 (+.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 10449 to 2660 computations (74.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.5b	(cbrt.f64 a)
	11.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series88.0ms (1.1%)

Counts

2 → 24

Calls

2 calls:

46.0ms	(cbrt.f64 a)
42.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune136.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	212	10	222

Error

0.1b

Counts

222 → 10

Alt Table

Status	Error	Program
	46.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) (cbrt.f64 a)))
✓	30.6b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	47.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	47.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (cbrt.f64 a)))
	46.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
▶	41.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
✓	31.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (cbrt.f64 a)))
	45.4b	(.f64 (/.f64 1 (/.f64 a (-.f64 (.f64 (neg.f64 b_2) (neg.f64 b_2)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))) (/.f64 1 (+.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 7378 to 1885 computations (74.5% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

series17.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
760×	`distribute-rgt-in_binary64`
722×	`distribute-lft-in_binary64`
150×	`associate-l_binary64`
141×	`distribute-lft-neg-out_binary64`

Counts

46 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	640
1	38	611
2	74	611
3	250	611
4	1127	611
5	5040	611

prune23.0ms (0.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	21	10	31

Error

0.1b

Counts

31 → 10

Alt Table

Status	Error	Program
	46.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) (cbrt.f64 a)))
✓	30.6b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	47.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	47.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (cbrt.f64 a)))
	46.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
✓	41.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
✓	31.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (cbrt.f64 a)))
	45.4b	(.f64 (/.f64 1 (/.f64 a (-.f64 (.f64 (neg.f64 b_2) (neg.f64 b_2)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))) (/.f64 1 (+.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))
	42.3b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 532 to 290 computations (45.5% saved)

regimes2.6s (31.3%)

Accuracy

Total 9.1b remaining (98.8%)

Threshold costs 0b (0%)

Counts

142 → 4

Compiler

Compiled 13963 to 8133 computations (41.8% saved)

bsearch91.0ms (1.1%)

Steps

Iters	Range		Point
6	2.2662785546022415e+101	2.240354704277509e+104	2.671050891722767e+102
9	-9.671766587169522e-132	-1.5906101622129874e-137	-4.848180454524789e-132
8	-1776253143368416000.0	-67071046155825.555	-1183068598468963.8

Compiler

Compiled 4 to 3 computations (25% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	82
1	54	82
2	69	82
3	83	82
4	90	82
5	93	82
6	94	82
7	94	82

end196.0ms (2.4%)

Compiler: Compiled 321 to 195 computations (39.3% saved)

Details

analyze279.0ms (3.4%)

sample2.2s (26.4%)

simplify84.0ms (1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series193.0ms (2.4%)

rewrite105.0ms (1.3%)

simplify191.0ms (2.3%)

prune279.0ms (3.4%)

localize13.0ms (0.2%)

series1.1s (13%)

rewrite54.0ms (0.7%)

simplify255.0ms (3.1%)

prune226.0ms (2.8%)

localize14.0ms (0.2%)

series88.0ms (1.1%)

rewrite8.0ms (0.1%)

simplify69.0ms (0.8%)

prune136.0ms (1.7%)

localize7.0ms (0.1%)

series17.0ms (0.2%)

rewrite1.0ms (0%)

simplify40.0ms (0.5%)

prune23.0ms (0.3%)

regimes2.6s (31.3%)

bsearch91.0ms (1.1%)

simplify15.0ms (0.2%)

end196.0ms (2.4%)

Profiling