Details

analyze753.0ms (9.5%)

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)

sample50.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	39×	body	2048	valid
11.0ms	164×	body	128	valid
7.0ms	23×	body	1024	valid
3.0ms	7×	body	4096	valid
3.0ms	14×	body	512	valid
1.0ms	9×	body	256	valid
1.0ms	13×	body	128	nan
0.0ms	7×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify331.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1261×	`associate-/l*_binary64`
1150×	`div-sub_binary64`
772×	`distribute-rgt-in_binary64`
702×	`distribute-lft-in_binary64`
619×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	32	24
2	65	24
3	128	24
4	178	24
5	287	24
6	460	24
7	754	24
8	1120	24
9	1142	24
10	1799	24
11	2162	24
12	1953	24
13	2041	24
14	2105	24
15	2131	24
16	2843	24
17	2603	24
18	2841	24
19	2951	24
20	3071	24
21	3113	24
22	3183	24
23	3171	24
24	3171	24
25	2191	24
26	2141	24
27	2105	24
28	2107	24
29	2107	24
30	2107	24
31	2107	24
32	1834	24

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

36.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.7b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite127.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

36.4b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1903 to 1105 computations (41.9% saved)

series166.0ms (2.1%)

Error

7.0b

Counts

4 → 68

Calls

4 calls:

47.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
36.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
34.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
29.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2756 to 1971 computations (28.5% saved)

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

508×	`times-frac_binary64`
408×	`associate-/l*_binary64`
323×	`div-sub_binary64`
301×	`associate-/r*_binary64`
183×	`distribute-rgt-in_binary64`

Counts

142 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3000
1	510	2750
2	1563	2744
3	4764	2744
4	5598	2744

prune58.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	9	120

Error

6.9b

Counts

120 → 9

Alt Table

Status	Error	Program
✓	36.7b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
	36.8b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
	39.8b	(neg.f64 (/.f64 c b))
	54.6b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))
	50.4b	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b) (.f64 a 2))) (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b) (*.f64 a 2))))
	43.9b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 a 2))
	37.5b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 a 2))
	47.8b	(/.f64 (neg.f64 b) a)
▶	36.8b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))

Compiler

Compiled 1980 to 1097 computations (44.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

rewrite289.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

693×	`times-frac_binary64`
439×	`add-sqr-sqrt_binary64`
364×	`*-un-lft-identity_binary64`
290×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`

Counts

4 → 356

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))
6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 11060 to 6512 computations (41.1% saved)

series165.0ms (2.1%)

Error

6.9b

Counts

4 → 68

Calls

4 calls:

50.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))
37.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
34.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
30.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))

Compiler

Compiled 2948 to 2163 computations (26.6% saved)

simplify424.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

490×	`associate-/l/_binary64`
316×	`associate-/r/_binary64`
228×	`*-commutative_binary64`
191×	`div-sub_binary64`
189×	`associate-*l/_binary64`

Counts

424 → 378

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	402	17406
1	912	16351
2	2881	16059
3	4706	16059
4	5204	16059

prune101.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	374	4	378
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	377	10	387

Error

6.9b

Counts

387 → 10

Alt Table

Status	Error	Program
	54.6b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))
	51.0b	(/.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (sqrt.f64 a) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))
✓	36.7b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
▶	36.8b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
	39.8b	(neg.f64 (/.f64 c b))
	37.5b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))) b) 2)))
	37.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2) (cbrt.f64 a)))
	43.9b	(/.f64 1 (/.f64 a (/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))) 2)))
	47.8b	(/.f64 (neg.f64 b) a)
✓	36.8b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))

Compiler

Compiled 4992 to 2715 computations (45.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite87.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

28×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`

Counts

4 → 83

Calls

4 calls:

11.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2202 to 1286 computations (41.6% saved)

series161.0ms (2%)

Error

6.9b

Counts

4 → 68

Calls

4 calls:

48.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
36.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
33.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
29.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2756 to 1971 computations (28.5% saved)

simplify125.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

421×	`times-frac_binary64`
381×	`associate-/l*_binary64`
293×	`distribute-rgt-in_binary64`
287×	`distribute-lft-in_binary64`
161×	`cancel-sign-sub-inv_binary64`

Counts

151 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	3242
1	543	2996
2	1788	2990
3	4880	2990
4	4944	2990

prune59.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	4	3	7
Picked	1	0	1
Done	1	1	2
Total	130	7	137

Error

6.9b

Counts

137 → 7

Alt Table

Status	Error	Program
✓	36.7b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
	39.8b	(neg.f64 (/.f64 c b))
	54.6b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))
	43.8b	(/.f64 (.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
	46.9b	(/.f64 (.f64 1/2 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b)))) (.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))
▶	36.9b	(.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	47.8b	(/.f64 (neg.f64 b) a)

Compiler

Compiled 2125 to 1167 computations (45.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (sqrt.f64 1/2) a)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

rewrite75.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

26×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
3.0ms	(/.f64 (sqrt.f64 1/2) a)
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 2211 to 1333 computations (39.7% saved)

series124.0ms (1.6%)

Error

6.9b

Counts

4 → 55

Calls

4 calls:

38.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
36.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
7.0ms	(/.f64 (sqrt.f64 1/2) a)

Compiler

Compiled 2619 to 1990 computations (24% saved)

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

607×	`associate-l_binary64`
525×	`associate-r_binary64`
323×	`unswap-sqr_binary64`
260×	`times-frac_binary64`
172×	`associate-/l*_binary64`

Counts

138 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2215
1	372	2098
2	972	2095
3	4006	2095
4	4932	2095

prune35.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	73	8	81

Error

6.9b

Counts

81 → 8

Alt Table

Status	Error	Program
	36.7b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
	39.8b	(neg.f64 (/.f64 c b))
	54.6b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))
	43.8b	(/.f64 (.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
	46.9b	(/.f64 (.f64 1/2 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b)))) (.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))
	48.0b	(.f64 (.f64 (*.f64 b -2) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	42.7b	(.f64 (.f64 (sqrt.f64 (.f64 c (.f64 a -4))) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	47.8b	(/.f64 (neg.f64 b) a)

Compiler

Compiled 1160 to 729 computations (37.2% saved)

regimes2.8s (34.8%)

Accuracy

Total 3.4b remaining (37.7%)

Threshold costs 0b (0%)

Compiler

Compiled 25092 to 17442 computations (30.5% saved)

bsearch114.0ms (1.4%)

Steps

Iters	Range		Point
7	9.657925202483324e+74	2.032011600382365e+77	3.480906013685845e+76
11	7.956215730584052e-120	7.301768186217896e-94	2.4654087246385048e-119
7	-9.093643705943827e+106	-4.17698357086546e+105	-3.061643530149749e+106

Compiler

Compiled 4 to 3 computations (25% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
20×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
17×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	104
1	73	104
2	100	104
3	125	104
4	143	104
5	156	104
6	165	104
7	173	104
8	177	104
9	178	104
10	177	104

end1.0ms (0%)

Compiler: Compiled 72 to 46 computations (36.1% saved)

sample1.7s (20.9%)

Algorithm

1×

intervals

Results

367.0ms	1128×	body	2048	valid
366.0ms	5206×	body	128	valid
197.0ms	756×	body	1024	valid
150.0ms	371×	body	4096	valid
70.0ms	369×	body	512	valid
41.0ms	618×	body	128	nan
25.0ms	359×	body	128	invalid
22.0ms	170×	body	256	valid

Compiler

Compiled 239 to 159 computations (33.5% saved)

Iter	Nodes	Cost
0	43	104
1	73	104
2	100	104
3	125	104
4	143	104
5	156	104
6	165	104
7	173	104
8	177	104
9	178	104
10	177	104

Iter	Nodes	Cost
0	43	104
1	73	104
2	100	104
3	125	104
4	143	104
5	156	104
6	165	104
7	173	104
8	177	104
9	178	104
10	177	104

Details

analyze753.0ms (9.5%)

sample50.0ms (0.6%)

simplify331.0ms (4.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite127.0ms (1.6%)

series166.0ms (2.1%)

simplify115.0ms (1.4%)

prune58.0ms (0.7%)

localize12.0ms (0.2%)

rewrite289.0ms (3.6%)

series165.0ms (2.1%)

simplify424.0ms (5.3%)

prune101.0ms (1.3%)

localize10.0ms (0.1%)

rewrite87.0ms (1.1%)

series161.0ms (2%)

simplify125.0ms (1.6%)

prune59.0ms (0.7%)

localize13.0ms (0.2%)

rewrite75.0ms (0.9%)

series124.0ms (1.6%)

simplify103.0ms (1.3%)

prune35.0ms (0.4%)

regimes2.8s (34.8%)

bsearch114.0ms (1.4%)

simplify11.0ms (0.1%)

end1.0ms (0%)

sample1.7s (20.9%)

Profiling

Iter	Nodes	Cost
0	43	104
1	73	104
2	100	104
3	125	104
4	143	104
5	156	104
6	165	104
7	173	104
8	177	104
9	178	104
10	177	104