Details

analyze350.0ms (3.8%)

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
37.4%	56.2%	6.4%	7
45.2%	48.4%	6.4%	8
49.1%	42.1%	8.7%	9
51.5%	35.1%	13.4%	10
58.1%	27.7%	14.2%	11
60.8%	22.6%	16.5%	12
62.3%	18.7%	19%	13
66.2%	14.4%	19.4%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample1.9s (20.4%)

Results

652.0ms	5576×	body	128	valid
497.0ms	1099×	body	2048	valid
241.0ms	697×	body	1024	valid
207.0ms	387×	body	4096	valid
92.0ms	332×	body	512	valid
70.0ms	614×	body	128	invalid
34.0ms	165×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify387.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

prune5.0ms (0.1%)

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

31.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	31.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	31.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (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))
✓	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	27.5b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series214.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

93.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
59.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
52.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite24.0ms (0.3%)

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:

11.0ms	(.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))

simplify193.0ms (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

prune226.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	222	9	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	224	9	233

Error

4.4b

Counts

233 → 9

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
	37.1b	(.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))
	40.7b	(/.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)))))))
	31.4b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
	39.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.4b	(/.f64 (neg.f64 b) a)
▶	29.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
	42.8b	(neg.f64 (/.f64 c b))
	35.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 6313 to 3694 computations (41.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
✓	0.2b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)
✓	13.0b	(sqrt.f64 (.f64 c (.f64 a -4)))

series436.0ms (4.7%)

Counts

3 → 24

Calls

3 calls:

249.0ms	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
161.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)
25.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
9×	`pow1_binary64`

Counts

3 → 69

Calls

3 calls:

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

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
316×	`fma-neg_binary64`
270×	`cancel-sign-sub-inv_binary64`
199×	`associate-/l/_binary64`
177×	`distribute-rgt-neg-in_binary64`

Counts

93 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	2709
1	553	2155
2	2037	2038
3	4525	2034
4	4956	2034
5	4874	2034

prune139.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	148	10	158

Error

2.7b

Counts

158 → 10

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
	37.1b	(.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))
▶	29.1b	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))
	39.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.4b	(/.f64 (neg.f64 b) a)
	29.4b	(.f64 (/.f64 1/2 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (cbrt.f64 a)))
✓	29.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
	42.8b	(neg.f64 (/.f64 c b))
	35.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	47.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)) a)

Compiler

Compiled 4143 to 2607 computations (37.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b))
✓	0.1b	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))
	0.2b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)
	13.0b	(sqrt.f64 (.f64 c (.f64 a -4)))

series850.0ms (9.1%)

Counts

2 → 24

Calls

2 calls:

598.0ms	(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b))
251.0ms	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 143

Calls

2 calls:

7.0ms	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))
4.0ms	(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b))

simplify136.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-/r/_binary64`
452×	`fma-def_binary64`
396×	`associate-/l/_binary64`
234×	`distribute-rgt-in_binary64`
218×	`distribute-lft-in_binary64`

Counts

167 → 280

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	322	6508
1	781	6173
2	2649	6099
3	5124	6099

prune359.0ms (3.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	362	1	363
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	362	11	373

Error

2.7b

Counts

373 → 11

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
	37.1b	(.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))
✓	29.1b	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))
	48.0b	(/.f64 1/2 (fma.f64 1/2 (/.f64 a b) (.f64 2 (/.f64 (.f64 a b) (.f64 -4 (.f64 c a))))))
	39.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.4b	(/.f64 (neg.f64 b) a)
▶	29.4b	(.f64 (/.f64 1/2 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (cbrt.f64 a)))
✓	29.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
	42.8b	(neg.f64 (/.f64 c b))
	35.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	47.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)) a)

Compiler

Compiled 11242 to 7020 computations (37.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/2 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.5b	(cbrt.f64 a)
	13.0b	(sqrt.f64 (.f64 c (.f64 a -4)))

series146.0ms (1.6%)

Counts

3 → 36

Calls

3 calls:

75.0ms	(/.f64 1/2 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
37.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
34.0ms	(cbrt.f64 a)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms	(/.f64 1/2 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

654×	`associate-*l/_binary64`
527×	`unswap-sqr_binary64`
450×	`fma-def_binary64`
362×	`associate-*r/_binary64`
351×	`associate-/r*_binary64`

Counts

114 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1257
1	173	1000
2	551	941
3	1754	926
4	4606	926
5	4896	926

prune137.0ms (1.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	170	12	182

Error

2.7b

Counts

182 → 12

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
	37.1b	(.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))
✓	29.1b	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))
	47.1b	(.f64 (/.f64 1/2 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 -4 a)))) b) (cbrt.f64 a)))
	48.0b	(/.f64 1/2 (fma.f64 1/2 (/.f64 a b) (.f64 2 (/.f64 (.f64 a b) (.f64 -4 (.f64 c a))))))
	39.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.4b	(/.f64 (neg.f64 b) a)
✓	29.4b	(.f64 (/.f64 1/2 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (cbrt.f64 a)))
✓	29.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
	42.8b	(neg.f64 (/.f64 c b))
	35.6b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	47.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)) a)

Compiler

Compiled 4556 to 2440 computations (46.4% saved)

regimes3.2s (34.1%)

Accuracy

Total 5.3b remaining (67.5%)

Threshold costs 0b (0%)

Counts

159 → 4

Compiler

Compiled 14220 to 9890 computations (30.5% saved)

bsearch110.0ms (1.2%)

Steps

Iters	Range	Point
11	2.2662785546022415e+101	2.7215606412094346e+129	6.283616353584907e+110
4	1.744071379683117e-178	2.8616850908874527e-178	2.2907073983447553e-178
7	-1.814430219754598e+156	-1.0182173360101637e+155	-1.0269296551259906e+155

Iters

Range

Point

2.2662785546022415e+101

2.7215606412094346e+129

6.283616353584907e+110

1.744071379683117e-178

2.8616850908874527e-178

2.2907073983447553e-178

-1.814430219754598e+156

-1.0182173360101637e+155

-1.0269296551259906e+155

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	87
1	65	85
2	80	85
3	95	85
4	102	85
5	105	85
6	106	85
7	105	85

end227.0ms (2.4%)

Compiler: Compiled 341 to 229 computations (32.8% saved)

Details

analyze350.0ms (3.8%)

sample1.9s (20.4%)

simplify387.0ms (4.2%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

series214.0ms (2.3%)

rewrite24.0ms (0.3%)

simplify193.0ms (2.1%)

prune226.0ms (2.4%)

localize9.0ms (0.1%)

series436.0ms (4.7%)

rewrite16.0ms (0.2%)

simplify112.0ms (1.2%)

prune139.0ms (1.5%)

localize12.0ms (0.1%)

series850.0ms (9.1%)

rewrite30.0ms (0.3%)

simplify136.0ms (1.5%)

prune359.0ms (3.9%)

localize13.0ms (0.1%)

series146.0ms (1.6%)

rewrite14.0ms (0.1%)

simplify72.0ms (0.8%)

prune137.0ms (1.5%)

regimes3.2s (34.1%)

bsearch110.0ms (1.2%)

simplify6.0ms (0.1%)

end227.0ms (2.4%)

Profiling