Details

analyze615.0ms (7%)

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)

sample129.0ms (1.5%)

Algorithm

1×

intervals

Results

12.0ms	167×	body	128	valid
11.0ms	32×	body	2048	valid
6.0ms	16×	body	4096	valid
6.0ms	23×	body	1024	valid
3.0ms	16×	body	512	valid
1.0ms	13×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify266.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	22

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

35.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	36.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
▶	35.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% 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))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	0.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	23.3b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series200.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

85.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
60.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
43.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
12.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify186.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
338×	`distribute-rgt-in_binary64`
273×	`cancel-sign-sub-inv_binary64`
155×	`associate-l_binary64`
153×	`associate-r_binary64`

Counts

205 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5424
1	673	4468
2	2524	4293
3	4550	4293
4	4991	4293
5	4994	4293
6	4884	4293

prune179.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	219	12	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	221	12	233

Error

7.9b

Counts

233 → 12

Alt Table

Status	Error	Program
	50.5b	(.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
	46.1b	(/.f64 (neg.f64 b) a)
▶	35.8b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) 1/2) a)
	38.9b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) (/.f64 1/2 a))
	37.0b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b))) (/.f64 1/2 a))
	40.1b	(neg.f64 (/.f64 c b))
	50.6b	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)) (sqrt.f64 (/.f64 1/2 a))) (.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) (sqrt.f64 (/.f64 1/2 a))))
	46.1b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	36.0b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (/.f64 1/2 a)))
	37.8b	(.f64 (+.f64 (fma.f64 (fabs.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) (neg.f64 b)) 0) (/.f64 1/2 a))
	41.1b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	40.4b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a))

Compiler

Compiled 6483 to 3818 computations (41.1% 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 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) 1/2) a)
	0.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	23.3b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series80.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

80.0ms

(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 25

Calls

1 calls:

6.0ms

(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
571×	`associate-/l*_binary64`
318×	`associate-/r*_binary64`
261×	`fma-def_binary64`
193×	`associate-/l/_binary64`

Counts

45 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1345
1	362	1205
2	1197	1156
3	4922	1156
4	4966	1156

prune154.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	206	11	217

Error

7.9b

Counts

217 → 11

Alt Table

Status	Error	Program
▶	35.1b	(/.f64 1 (/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
	50.5b	(.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
	46.1b	(/.f64 (neg.f64 b) a)
	41.1b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	37.0b	(/.f64 (.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b))) 1/2) a)
	40.4b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a))
	35.8b	(/.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) (neg.f64 b)) 1/2) a)
	36.0b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (/.f64 1/2 a)))
	40.1b	(neg.f64 (/.f64 c b))
	46.1b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	38.8b	(/.f64 (.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) 1/2) a)

Compiler

Compiled 5582 to 3251 computations (41.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
✓	0.1b	(/.f64 1 (/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
✓	0.4b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
✓	15.4b	(sqrt.f64 (.f64 a (.f64 c -4)))

series805.0ms (9.1%)

Counts

4 → 36

Calls

4 calls:

412.0ms	(/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
231.0ms	(/.f64 1 (/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
142.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
20.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
30×	`add-exp-log_binary64`

Counts

4 → 135

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
6.0ms	(/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
3.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
3.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify161.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
331×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-neg-in_binary64`
180×	`times-frac_binary64`

Counts

171 → 262

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	297	5470
1	722	4595
2	2707	4410
3	4708	4405
4	4952	4405
5	4880	4405

prune204.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	265	8	273

Error

2.9b

Counts

273 → 8

Alt Table

Status	Error	Program
	46.1b	(/.f64 (neg.f64 b) a)
	46.6b	(/.f64 1 (/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4)))) b))))
	39.9b	(/.f64 1 (fma.f64 4 (/.f64 b (*.f64 -4 c)) (/.f64 a b)))
▶	35.2b	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
	40.1b	(neg.f64 (/.f64 c b))
	41.1b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	35.8b	(/.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) (neg.f64 b)) 1/2) a)
	38.8b	(/.f64 (.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) 1/2) a)

Compiler

Compiled 7618 to 5002 computations (34.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
✓	0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
	0.4b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
	15.4b	(sqrt.f64 (.f64 a (.f64 c -4)))

series625.0ms (7.1%)

Counts

2 → 24

Calls

2 calls:

392.0ms	(/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
232.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
102×	`add-cube-cbrt_binary64`
96×	`add-exp-log_binary64`

Counts

2 → 219

Calls

2 calls:

10.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
5.0ms	(/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))

simplify258.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-/l/_binary64`
364×	`distribute-rgt-in_binary64`
350×	`fma-def_binary64`
344×	`distribute-lft-in_binary64`
196×	`fma-neg_binary64`

Counts

243 → 313

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	280	9434
1	723	8491
2	2185	8222
3	4908	8218
4	4994	8218
5	4937	8218

prune309.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	395	1	396
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	395	9	404

Error

2.9b

Counts

404 → 9

Alt Table

Status	Error	Program
	46.6b	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c)))) b))))
	46.1b	(/.f64 (neg.f64 b) a)
	46.6b	(/.f64 1 (/.f64 a (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4)))) b))))
	39.9b	(/.f64 1 (fma.f64 4 (/.f64 b (*.f64 -4 c)) (/.f64 a b)))
✓	35.2b	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))))
	40.1b	(neg.f64 (/.f64 c b))
	41.1b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	35.8b	(/.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) (neg.f64 b)) 1/2) a)
	38.8b	(/.f64 (.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) 1/2) a)

Compiler

Compiled 12875 to 8860 computations (31.2% saved)

regimes2.7s (31%)

Accuracy

Total 5.8b remaining (66.6%)

Threshold costs 0b (0%)

Counts

213 → 4

Compiler

Compiled 18064 to 12958 computations (28.3% saved)

bsearch105.0ms (1.2%)

Steps

Iters	Range	Point
8	3.7345201917185293e+76	1.5822281521112962e+80	2.980663629993403e+79
8	3.0176733300357244e-180	4.113794117348541e-177	3.504400908400674e-178
8	-2.5495692589417495e+117	-3.525996866042671e+114	-3.738191357919323e+116

Iters

Range

Point

3.7345201917185293e+76

1.5822281521112962e+80

2.980663629993403e+79

3.0176733300357244e-180

4.113794117348541e-177

3.504400908400674e-178

-2.5495692589417495e+117

-3.525996866042671e+114

-3.738191357919323e+116

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	85
1	56	83
2	64	83
3	70	83
4	72	83
5	70	83

end1.0ms (0%)

Compiler: Compiled 59 to 37 computations (37.3% saved)

sample1.6s (18.1%)

Algorithm

1×

intervals

Results

359.0ms	1134×	body	2048	valid
344.0ms	5234×	body	128	valid
172.0ms	696×	body	1024	valid
169.0ms	425×	body	4096	valid
70.0ms	358×	body	512	valid
43.0ms	668×	body	128	nan
24.0ms	374×	body	128	invalid
19.0ms	153×	body	256	valid

Compiler

Compiled 244 to 173 computations (29.1% saved)

Details

analyze615.0ms (7%)

sample129.0ms (1.5%)

simplify266.0ms (3%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series200.0ms (2.3%)

rewrite22.0ms (0.2%)

simplify186.0ms (2.1%)

prune179.0ms (2%)

localize9.0ms (0.1%)

series80.0ms (0.9%)

rewrite8.0ms (0.1%)

simplify62.0ms (0.7%)

prune154.0ms (1.7%)

localize10.0ms (0.1%)

series805.0ms (9.1%)

rewrite28.0ms (0.3%)

simplify161.0ms (1.8%)

prune204.0ms (2.3%)

localize11.0ms (0.1%)

series625.0ms (7.1%)

rewrite49.0ms (0.5%)

simplify258.0ms (2.9%)

prune309.0ms (3.5%)

regimes2.7s (31%)

bsearch105.0ms (1.2%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.6s (18.1%)

Profiling