Details

analyze648.0ms (8.6%)

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)

sample187.0ms (2.5%)

Algorithm

1×

intervals

Results

16.0ms	38×	body	2048	valid
11.0ms	166×	body	128	valid
7.0ms	27×	body	1024	valid
2.0ms	13×	body	512	valid
2.0ms	6×	body	4096	valid
1.0ms	14×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify128.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

36.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	1.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.3b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series193.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
52.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
50.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
11.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 77

Calls

4 calls:

5.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 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))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
539×	`associate-/l*_binary64`
468×	`fma-def_binary64`
198×	`cancel-sign-sub-inv_binary64`
125×	`associate-/r/_binary64`

Counts

173 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3876
1	521	3658
2	1578	3494
3	5011	3494

prune147.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	185	8	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	9	194

Error

5.2b

Counts

194 → 9

Alt Table

Status	Error	Program
	36.4b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	39.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
▶	33.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))))))
	43.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	52.0b	(.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (.f64 4 (/.f64 (.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
✓	36.3b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	47.2b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a))
	43.3b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	51.1b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a))))

Compiler

Compiled 5149 to 3115 computations (39.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
✓	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
✓	15.1b	(sqrt.f64 (.f64 c (.f64 a -4)))

series749.0ms (9.9%)

Counts

4 → 42

Calls

4 calls:

382.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))
208.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
139.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
20.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
99×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

4 → 164

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
4.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))

simplify154.0ms (2%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-neg_binary64`
501×	`fma-def_binary64`
444×	`associate-/r/_binary64`
326×	`cancel-sign-sub-inv_binary64`
212×	`associate-/l/_binary64`

Counts

206 → 291

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	6330
1	647	5816
2	2220	5699
3	4541	5689
4	4933	5689

prune229.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	290	10	300

Error

2.2b

Counts

300 → 10

Alt Table

Status	Error	Program
▶	33.4b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
	52.0b	(.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (.f64 4 (/.f64 (.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
	45.6b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))))))))
	39.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	47.2b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a))
	43.3b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	45.9b	(.f64 -1/2 (/.f64 1 (fma.f64 1/8 (/.f64 (.f64 a (.f64 -4 (.f64 c a))) (pow.f64 b 3)) (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b))))))
	39.2b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (.f64 -4 c) b)))))
	49.4b	(.f64 -1/2 (/.f64 1 (.f64 (sqrt.f64 a) (/.f64 (sqrt.f64 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))))

Compiler

Compiled 9135 to 6056 computations (33.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 c a))
✓	0.2b	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
✓	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
✓	15.1b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series379.0ms (5%)

Counts

4 → 28

Calls

4 calls:

208.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
145.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
21.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
5.0ms	(.f64 -4 (.f64 c a))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64`
17×	`pow1_binary64`
16×	`associate-l_binary64`

Counts

4 → 95

Calls

4 calls:

8.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
4.0ms	(.f64 -4 (.f64 c a))
3.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/r*_binary64`
447×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`
157×	`associate-r_binary64`

Counts

123 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	2765
1	587	2488
2	1863	2447
3	4942	2447
4	4995	2447
5	4936	2447

prune132.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	167	10	177

Error

2.2b

Counts

177 → 10

Alt Table

Status	Error	Program
	45.4b	(.f64 -1/2 (fma.f64 1/8 (/.f64 16 (.f64 (pow.f64 b 3) (/.f64 1 (.f64 c (.f64 c a))))) (.f64 -1/2 (/.f64 (.f64 -4 c) b))))
✓	33.4b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
	45.6b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))))))))
▶	39.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	47.2b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a))
	43.3b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	45.9b	(.f64 -1/2 (/.f64 1 (fma.f64 1/8 (/.f64 (.f64 a (.f64 -4 (.f64 c a))) (pow.f64 b 3)) (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b))))))
	39.2b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (.f64 -4 c) b)))))
	49.4b	(.f64 -1/2 (/.f64 1 (.f64 (sqrt.f64 a) (/.f64 (sqrt.f64 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))))

Compiler

Compiled 4827 to 3099 computations (35.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(.f64 -1/2 (.f64 2 (/.f64 c b)))
7.0ms	(*.f64 2 (/.f64 c b))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
14×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 57

Calls

2 calls:

7.0ms	(.f64 -1/2 (.f64 2 (/.f64 c b)))
5.0ms	(*.f64 2 (/.f64 c b))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

538×	`associate-/l/_binary64`
505×	`associate-l_binary64`
398×	`neg-mul-1_binary64`
364×	`associate-r_binary64`
330×	`times-frac_binary64`

Counts

81 → 84

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	102	758
1	217	669
2	634	669
3	2292	669
4	4278	669
5	5225	669

prune52.0ms (0.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	84	10	94

Error

2.2b

Counts

94 → 10

Alt Table

Status	Error	Program
	45.4b	(.f64 -1/2 (fma.f64 1/8 (/.f64 16 (.f64 (pow.f64 b 3) (/.f64 1 (.f64 c (.f64 c a))))) (.f64 -1/2 (/.f64 (.f64 -4 c) b))))
✓	33.4b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
	45.6b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))))))))
✓	39.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.6b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	47.2b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a))
	43.3b	(.f64 -1/2 (.f64 2 (/.f64 b a)))
	45.9b	(.f64 -1/2 (/.f64 1 (fma.f64 1/8 (/.f64 (.f64 a (.f64 -4 (.f64 c a))) (pow.f64 b 3)) (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b))))))
	39.2b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (.f64 -4 c) b)))))
	49.4b	(.f64 -1/2 (/.f64 1 (.f64 (sqrt.f64 a) (/.f64 (sqrt.f64 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))))

Compiler

Compiled 1224 to 747 computations (39% saved)

regimes2.3s (30.9%)

Accuracy

Total 7.8b remaining (71.2%)

Threshold costs 0b (0%)

Counts

148 → 4

Compiler

Compiled 13528 to 9618 computations (28.9% saved)

bsearch97.0ms (1.3%)

Steps

Iters	Range		Point
7	1.4207986499139543e+94	2.937033851030537e+95	2.4136909489838122e+95
8	1.075417421308706e-54	5.973866601528205e-52	1.0870661076768719e-54
9	-1.2284966536175126e-135	-1.437779468124281e-141	-1.1094489260975471e-135

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
14×	`+-commutative_binary64`
12×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	90
1	65	90
2	82	90
3	103	90
4	114	90
5	120	90
6	122	90
7	120	90

end1.0ms (0%)

Compiler: Compiled 63 to 39 computations (38.1% saved)

sample1.7s (22.8%)

Algorithm

1×

intervals

Results

375.0ms	5295×	body	128	valid
373.0ms	1098×	body	2048	valid
188.0ms	681×	body	1024	valid
162.0ms	371×	body	4096	valid
72.0ms	375×	body	512	valid
55.0ms	705×	body	128	nan
31.0ms	361×	body	128	invalid
25.0ms	180×	body	256	valid

Compiler

Compiled 291 to 207 computations (28.9% saved)

Details

analyze648.0ms (8.6%)

sample187.0ms (2.5%)

simplify128.0ms (1.7%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series193.0ms (2.6%)

rewrite15.0ms (0.2%)

simplify84.0ms (1.1%)

prune147.0ms (2%)

localize11.0ms (0.1%)

series749.0ms (9.9%)

rewrite32.0ms (0.4%)

simplify154.0ms (2%)

prune229.0ms (3%)

localize10.0ms (0.1%)

series379.0ms (5%)

rewrite23.0ms (0.3%)

simplify103.0ms (1.4%)

prune132.0ms (1.8%)

localize4.0ms (0.1%)

series16.0ms (0.2%)

rewrite15.0ms (0.2%)

simplify58.0ms (0.8%)

prune52.0ms (0.7%)

regimes2.3s (30.9%)

bsearch97.0ms (1.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (22.8%)

Profiling