Details

analyze337.0ms (4.4%)

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)

sample2.1s (27.8%)

Results

859.0ms	5576×	body	128	valid
536.0ms	1099×	body	2048	valid
239.0ms	697×	body	1024	valid
209.0ms	387×	body	4096	valid
91.0ms	332×	body	512	valid
73.0ms	614×	body	128	invalid
31.0ms	165×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify260.0ms (3.4%)

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

prune4.0ms (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

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 (.f64 4 a) c)))) (.f64 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))
✓	0.8b	(-.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)))

series198.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

83.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
54.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
49.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
12.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite23.0ms (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:

8.0ms	(.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))

simplify200.0ms (2.6%)

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

prune209.0ms (2.7%)

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)

localize11.0ms (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)))

series410.0ms (5.3%)

Counts

3 → 24

Calls

3 calls:

235.0ms	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
152.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)
22.0ms	(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:

7.0ms	(/.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)))

simplify109.0ms (1.4%)

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

prune153.0ms (2%)

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))
	47.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)) a)
	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))
▶	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))

Compiler

Compiled 4143 to 2607 computations (37.1% saved)

localize10.0ms (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)))

series664.0ms (8.6%)

Counts

2 → 24

Calls

2 calls:

417.0ms	(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b))
247.0ms	(/.f64 1/2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b)))

rewrite30.0ms (0.4%)

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:

8.0ms	(/.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))

simplify146.0ms (1.9%)

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

prune317.0ms (4.1%)

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))
	48.0b	(/.f64 1/2 (fma.f64 1/2 (/.f64 a b) (.f64 2 (/.f64 (.f64 a b) (.f64 -4 (.f64 c 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)))
	47.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)) a)
	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))
✓	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)
✓	29.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
	42.8b	(neg.f64 (/.f64 c b))

Compiler

Compiled 11242 to 7020 computations (37.6% saved)

localize12.0ms (0.2%)

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)))

series148.0ms (1.9%)

Counts

3 → 36

Calls

3 calls:

74.0ms	(/.f64 1/2 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
38.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
36.0ms	(cbrt.f64 a)

rewrite13.0ms (0.2%)

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 (cbrt.f64 a) (cbrt.f64 a))
4.0ms	(/.f64 1/2 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms	(cbrt.f64 a)

simplify80.0ms (1%)

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

prune131.0ms (1.7%)

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))
	48.0b	(/.f64 1/2 (fma.f64 1/2 (/.f64 a b) (.f64 2 (/.f64 (.f64 a b) (.f64 -4 (.f64 c 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)))
	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)))
✓	29.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)) a)
	47.0b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)) a)
	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))
✓	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)
	42.8b	(neg.f64 (/.f64 c b))

Compiler

Compiled 4556 to 2440 computations (46.4% saved)

regimes1.8s (23.4%)

Accuracy

Total 5.3b remaining (67.5%)

Threshold costs 0b (0%)

Counts

159 → 4

Compiler

Compiled 14220 to 9890 computations (30.5% saved)

bsearch101.0ms (1.3%)

Steps

Iters	Range	Point
11	2.2662785546022415e+101	2.7215606412094346e+129	6.283616353584907e+110
4	1.744071379683117e-178	2.8616850908874527e-178	2.4057886654314162e-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

2.4057886654314162e-178

-1.814430219754598e+156

-1.0182173360101637e+155

-1.0269296551259906e+155

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`
10×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	87
1	65	85
2	83	85
3	98	85
4	109	85
5	119	85
6	124	85
7	126	85
8	124	85

end159.0ms (2.1%)

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

Details

analyze337.0ms (4.4%)

sample2.1s (27.8%)

simplify260.0ms (3.4%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series198.0ms (2.6%)

rewrite23.0ms (0.3%)

simplify200.0ms (2.6%)

prune209.0ms (2.7%)

localize11.0ms (0.1%)

series410.0ms (5.3%)

rewrite16.0ms (0.2%)

simplify109.0ms (1.4%)

prune153.0ms (2%)

localize10.0ms (0.1%)

series664.0ms (8.6%)

rewrite30.0ms (0.4%)

simplify146.0ms (1.9%)

prune317.0ms (4.1%)

localize12.0ms (0.2%)

series148.0ms (1.9%)

rewrite13.0ms (0.2%)

simplify80.0ms (1%)

prune131.0ms (1.7%)

regimes1.8s (23.4%)

bsearch101.0ms (1.3%)

simplify8.0ms (0.1%)

end159.0ms (2.1%)

Profiling