Details

analyze739.0ms (11.3%)

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
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)

sample51.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	39×	body	2048	valid
11.0ms	164×	body	128	valid
6.0ms	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)

simplify316.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1228×	`associate-/l*_binary64`
1150×	`div-sub_binary64`
630×	`distribute-rgt-in_binary64`
619×	`times-frac_binary64`
588×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	24
2	62	24
3	121	24
4	172	24
5	282	24
6	460	24
7	748	24
8	1084	24
9	1128	24
10	1799	24
11	2594	24
12	2001	24
13	2089	24
14	2153	24
15	2179	24
16	2431	24
17	2909	24
18	2913	24
19	2991	24
20	3053	24
21	3065	24
22	3035	24
23	3211	24
24	3211	24
25	2043	24
26	2195	24
27	2097	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 4 (.f64 a c)))) b) (.f64 a 2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite121.0ms (1.8%)

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:

8.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1903 to 985 computations (48.2% saved)

series183.0ms (2.8%)

Error

7.0b

Counts

4 → 68

Calls

4 calls:

55.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
40.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
34.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
34.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2756 to 1971 computations (28.5% saved)

simplify121.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
417×	`associate-/l*_binary64`
326×	`div-sub_binary64`
303×	`associate-/r*_binary64`
180×	`distribute-rgt-in_binary64`

Counts

142 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2994
1	504	2750
2	1518	2744
3	4742	2744
4	5581	2744

prune63.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	9	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Error

6.9b

Counts

120 → 9

Alt Table

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

Compiler

Compiled 1999 to 1099 computations (45% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

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 → 73

Calls

4 calls:

8.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4)))) b) (.f64 a 2))
6.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))) b)
3.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))
3.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4))))

Compiler

Compiled 1885 to 1094 computations (42% saved)

series171.0ms (2.6%)

Error

6.9b

Counts

4 → 68

Calls

4 calls:

48.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4)))) b) (.f64 a 2))
40.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))) b)
39.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4))))
31.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))

Compiler

Compiled 2756 to 1971 computations (28.5% saved)

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

511×	`times-frac_binary64`
251×	`distribute-rgt-in_binary64`
244×	`cancel-sign-sub-inv_binary64`
235×	`distribute-lft-in_binary64`
231×	`div-sub_binary64`

Counts

141 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2986
1	521	2736
2	1750	2721
3	4480	2721
4	5112	2721

prune47.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	117	9	126

Error

6.9b

Counts

126 → 9

Alt Table

Status	Error	Program
	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))))
	47.8b	(/.f64 (neg.f64 b) a)
	39.8b	(neg.f64 (/.f64 c b))
✓	36.7b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4)))) b) (.f64 a 2))
	54.6b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.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))
▶	32.1b	(/.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 a 2))
	36.8b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	36.8b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b) 2)))

Compiler

Compiled 1946 to 1091 computations (43.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
2.8b	(/.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 a 2))
10.4b	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

rewrite133.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

54×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
21×	`associate-/l*_binary64`

Counts

4 → 118

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 a 2))
12.0ms	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))

Compiler

Compiled 4500 to 2676 computations (40.5% saved)

series221.0ms (3.4%)

Error

6.9b

Counts

4 → 68

Calls

4 calls:

66.0ms	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))))
60.0ms	(/.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 a 2))
38.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
37.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))

Compiler

Compiled 3668 to 2581 computations (29.6% saved)

simplify185.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

309×	`div-sub_binary64`
276×	`associate-/l*_binary64`
240×	`cancel-sign-sub-inv_binary64`
222×	`times-frac_binary64`
155×	`log-div_binary64`

Counts

186 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	5851
1	714	5232
2	2949	5185
3	4762	5185
4	4913	5185

prune81.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	158	7	165

Error

6.9b

Counts

165 → 7

Alt Table

Status	Error	Program
	40.2b	(/.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (*.f64 a 2))
✓	36.7b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4)))) b) (.f64 a 2))
	43.9b	(.f64 2 (-.f64 (/.f64 (.f64 c b) (.f64 c (.f64 a -4))) (/.f64 c (sqrt.f64 (.f64 c (.f64 a -4))))))
	47.8b	(/.f64 (neg.f64 b) a)
	39.8b	(neg.f64 (/.f64 c b))
▶	32.1b	(/.f64 1 (/.f64 a (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))))
	32.1b	(.f64 (/.f64 1 a) (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))))

Compiler

Compiled 3562 to 2070 computations (41.9% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
2.9b	(/.f64 a (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))))))
10.5b	(/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

rewrite79.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

9.0ms	(/.f64 a (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))))))
7.0ms	(/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))

Compiler

Compiled 2593 to 1308 computations (49.6% saved)

series416.0ms (6.3%)

Error

6.9b

Counts

4 → 70

Calls

4 calls:

277.0ms	(/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))
51.0ms	(/.f64 a (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))))))
37.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))

Compiler

Compiled 3553 to 2451 computations (31% saved)

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

800×	`associate-/r/_binary64`
535×	`associate-/l/_binary64`
193×	`cancel-sign-sub-inv_binary64`
189×	`distribute-rgt-neg-in_binary64`
184×	`distribute-rgt-in_binary64`

Counts

148 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3597
1	607	3079
2	2176	2975
3	5405	2975

prune42.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Error

6.9b

Counts

107 → 7

Alt Table

Status	Error	Program
	40.2b	(/.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (*.f64 a 2))
	36.7b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4)))) b) (.f64 a 2))
	43.9b	(.f64 2 (-.f64 (/.f64 (.f64 c b) (.f64 c (.f64 a -4))) (/.f64 c (sqrt.f64 (.f64 c (.f64 a -4))))))
	47.8b	(/.f64 (neg.f64 b) a)
	39.8b	(neg.f64 (/.f64 c b))
	32.1b	(/.f64 1 (/.f64 a (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))))
	32.1b	(.f64 (/.f64 1 a) (.f64 -2 (/.f64 (.f64 c a) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))))

Compiler

Compiled 1433 to 803 computations (44% saved)

regimes1.4s (20.9%)

Accuracy

Total 1.3b remaining (18.6%)

Threshold costs 0b (0%)

Compiler

Compiled 13500 to 8994 computations (33.4% saved)

bsearch94.0ms (1.4%)

Steps

Iters	Range	Point
7	9.657925202483324e+74	2.032011600382365e+77	1.9972411182687842e+77
9	-5.061462832048152e-162	-9.280557748819019e-169	-9.859859419540874e-169
7	-9.093643705943827e+106	-4.17698357086546e+105	-3.061643530149749e+106

Iters

Range

Point

9.657925202483324e+74

2.032011600382365e+77

1.9972411182687842e+77

-5.061462832048152e-162

-9.280557748819019e-169

-9.859859419540874e-169

-9.093643705943827e+106

-4.17698357086546e+105

-3.061643530149749e+106

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	94
1	58	94
2	77	94
3	95	94
4	105	94
5	109	94
6	110	94
7	108	94

end1.0ms (0%)

Compiler: Compiled 66 to 41 computations (37.9% saved)

sample1.8s (26.7%)

Algorithm

1×

intervals

Results

395.0ms	1128×	body	2048	valid
366.0ms	5206×	body	128	valid
202.0ms	756×	body	1024	valid
154.0ms	371×	body	4096	valid
76.0ms	369×	body	512	valid
44.0ms	618×	body	128	nan
24.0ms	359×	body	128	invalid
23.0ms	170×	body	256	valid

Compiler

Compiled 219 to 147 computations (32.9% saved)

Details

analyze739.0ms (11.3%)

sample51.0ms (0.8%)

simplify316.0ms (4.8%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite121.0ms (1.8%)

series183.0ms (2.8%)

simplify121.0ms (1.9%)

prune63.0ms (1%)

localize12.0ms (0.2%)

rewrite77.0ms (1.2%)

series171.0ms (2.6%)

simplify119.0ms (1.8%)

prune47.0ms (0.7%)

localize15.0ms (0.2%)

rewrite133.0ms (2%)

series221.0ms (3.4%)

simplify185.0ms (2.8%)

prune81.0ms (1.2%)

localize28.0ms (0.4%)

rewrite79.0ms (1.2%)

series416.0ms (6.3%)

simplify99.0ms (1.5%)

prune42.0ms (0.6%)

regimes1.4s (20.9%)

bsearch94.0ms (1.4%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.8s (26.7%)

Profiling