Details

analyze633.0ms (4.9%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (18.2%)

Results

657.0ms	5385×	body	128	valid
515.0ms	1110×	body	2048	valid
379.0ms	784×	body	1024	valid
218.0ms	397×	body	4096	valid
121.0ms	1060×	body	128	invalid
112.0ms	387×	body	512	valid
39.0ms	193×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
205×	`fma-def_binary64`
183×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.4b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series510.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

334.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
126.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
41.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
60×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 176

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
8.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify262.0ms (2%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
181×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
135×	`associate-r_binary64`

Counts

272 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	8791
1	779	6792
2	2682	5750
3	4584	5750
4	4974	5750

prune230.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	282	10	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	283	10	293

Error

5.3b

Counts

293 → 10

Alt Table

Status	Error	Program
	45.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 a)) (sqrt.f64 a))
	32.4b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
	46.5b	(/.f64 (*.f64 -2 b_2) a)
	46.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	33.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	31.5b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
▶	30.5b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	32.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
	41.1b	(*.f64 -1/2 (/.f64 c b_2))
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 9072 to 1998 computations (78% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	0.1b	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
✓	0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
✓	12.1b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series877.0ms (6.7%)

Counts

4 → 42

Calls

4 calls:

436.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
218.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
160.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
63.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite73.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`*-un-lft-identity_binary64`
162×	`times-frac_binary64`
139×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
34×	`distribute-lft-out--_binary64`

Counts

4 → 244

Calls

4 calls:

8.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
5.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
5.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify252.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
401×	`fma-neg_binary64`
292×	`cancel-sign-sub-inv_binary64`
186×	`sub-neg_binary64`
153×	`distribute-frac-neg_binary64`

Counts

286 → 378

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	9160
1	794	8172
2	2705	7612
3	4798	7608
4	4906	7608

prune248.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	374	4	378
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	379	9	388

Error

0.1b

Counts

388 → 9

Alt Table

Status	Error	Program
	42.9b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	40.8b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
	45.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 a)) (sqrt.f64 a))
	48.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
	33.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	45.6b	(.f64 (/.f64 (-.f64 (pow.f64 (neg.f64 b_2) 3) (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a c))) b_2) 3)) a) (/.f64 1 (fma.f64 b_2 b_2 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a c))) b_2) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) b_2) b_2)))))
▶	32.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
	41.1b	(*.f64 -1/2 (/.f64 c b_2))
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 11634 to 2943 computations (74.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
✓	0.1b	(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a)
✓	3.1b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
	12.1b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series507.0ms (3.9%)

Counts

3 → 42

Calls

3 calls:

217.0ms	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
177.0ms	(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a)
113.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

rewrite182.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

760×	`times-frac_binary64`
554×	`*-un-lft-identity_binary64`
552×	`add-sqr-sqrt_binary64`
540×	`add-cube-cbrt_binary64`
442×	`prod-diff_binary64`

Counts

3 → 556

Calls

3 calls:

36.0ms	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
2.0ms	(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a)
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify693.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

363×	`unsub-neg_binary64`
346×	`fma-neg_binary64`
336×	`fma-udef_binary64`
263×	`associate-+r-_binary64`
252×	`sub-neg_binary64`

Counts

598 → 641

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	649	44671
1	1436	26739
2	3109	19131
3	4699	18687
4	4836	18687

prune333.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	666	2	668
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	666	11	677

Error

0.0b

Counts

677 → 11

Alt Table

Status	Error	Program
	42.9b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	40.8b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
	45.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 a)) (sqrt.f64 a))
	48.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
	43.2b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) a))
	41.1b	(*.f64 -1/2 (/.f64 c b_2))
▶	33.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	45.6b	(.f64 (/.f64 (-.f64 (pow.f64 (neg.f64 b_2) 3) (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a c))) b_2) 3)) a) (/.f64 1 (fma.f64 b_2 b_2 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a c))) b_2) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) b_2) b_2)))))
✓	32.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
	49.4b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) a))
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 40106 to 5394 computations (86.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	1.8b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
✓	6.4b	(/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	12.1b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.0s (7.9%)

Counts

3 → 36

Calls

3 calls:

459.0ms

(/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

424.0ms

(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)

141.0ms

(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 125

Calls

3 calls:

8.0ms

(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)

5.0ms

(/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

3.0ms

(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)

simplify179.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
390×	`cancel-sign-sub-inv_binary64`
251×	`fma-neg_binary64`
247×	`times-frac_binary64`
196×	`associate-/l*_binary64`

Counts

161 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	5674
1	872	4918
2	3266	4799
3	4807	4797
4	4966	4797
5	4909	4797

prune145.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	263	11	274

Error

0.0b

Counts

274 → 11

Alt Table

Status	Error	Program
	42.9b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	40.8b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
	45.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 a)) (sqrt.f64 a))
	48.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
	30.4b	(.f64 1 (/.f64 c (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))
✓	32.3b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a))
	43.2b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) a))
	41.1b	(*.f64 -1/2 (/.f64 c b_2))
	33.6b	(.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 1 a))
	49.4b	(-.f64 (/.f64 (neg.f64 b_2) a) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) a))
	46.5b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 7615 to 1813 computations (76.2% saved)

regimes4.0s (30.7%)

Accuracy

Total 8.5b remaining (99.1%)

Threshold costs 0b (0%)

Counts

240 → 4

Compiler

Compiled 21523 to 12761 computations (40.7% saved)

bsearch124.0ms (1%)

Steps

Iters	Range		Point
9	3.0962393092803596e+73	3.776391433211697e+78	3.465292549325922e+78
7	1.2370316317046848e-196	2.671735367293227e-194	1.5302979495318542e-196
9	-1.7467681364277589e+44	-1.0267853400405548e+37	-5.134717094691006e+37

Compiler

Compiled 4 to 3 computations (25% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	76
1	55	76
2	69	76
3	83	76
4	90	76
5	93	76
6	94	76
7	93	76

end161.0ms (1.2%)

Compiler: Compiled 291 to 186 computations (36.1% saved)

Details

analyze633.0ms (4.9%)

sample2.4s (18.2%)

simplify84.0ms (0.6%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series510.0ms (3.9%)

rewrite47.0ms (0.4%)

simplify262.0ms (2%)

prune230.0ms (1.8%)

localize10.0ms (0.1%)

series877.0ms (6.7%)

rewrite73.0ms (0.6%)

simplify252.0ms (1.9%)

prune248.0ms (1.9%)

localize12.0ms (0.1%)

series507.0ms (3.9%)

rewrite182.0ms (1.4%)

simplify693.0ms (5.3%)

prune333.0ms (2.6%)

localize11.0ms (0.1%)

series1.0s (7.9%)

rewrite26.0ms (0.2%)

simplify179.0ms (1.4%)

prune145.0ms (1.1%)

regimes4.0s (30.7%)

bsearch124.0ms (1%)

simplify15.0ms (0.1%)

end161.0ms (1.2%)

Profiling