Details

analyze1.7s (21%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.5s (18%)

Results

1.1s	8256×	body	128	valid
187.0ms	253×	body	8192	exit
33.0ms	250×	body	128	invalid

Compiler

Compiled 39 to 23 computations (41% saved)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

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

26.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (.f64 b c) (.f64 a d))
✓	26.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series103.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

93.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
10.0ms	(-.f64 (.f64 b c) (.f64 a d))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-neg_binary64`
380×	`associate-l_binary64`
348×	`fma-def_binary64`
315×	`associate-r_binary64`
247×	`associate-/l*_binary64`

Counts

144 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2762
1	323	2614
2	1084	2567
3	4430	2567
4	4952	2567

prune74.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Error

1.4b

Counts

110 → 7

Alt Table

Status	Error	Program
	27.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	34.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	40.1b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	40.5b	(neg.f64 (/.f64 a d))
▶	17.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	17.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)))
	34.2b	(/.f64 b c)

Compiler

Compiled 2769 to 585 computations (78.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.7b	(-.f64 (.f64 c b) (.f64 a d))
✓	16.1b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series241.0ms (2.9%)

Counts

4 → 132

Calls

4 calls:

108.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
104.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
19.0ms	(/.f64 1 (hypot.f64 d c))
10.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 139

Calls

4 calls:

11.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
5.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
3.0ms	(-.f64 (.f64 c b) (.f64 a d))
2.0ms	(/.f64 1 (hypot.f64 d c))

simplify129.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
537×	`fma-def_binary64`
368×	`cancel-sign-sub-inv_binary64`
196×	`fma-neg_binary64`
181×	`sub-neg_binary64`

Counts

271 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	6415
1	744	5877
2	2552	5818
3	5061	5818

prune193.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	264	7	271
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	267	11	278

Error

1.4b

Counts

278 → 11

Alt Table

Status	Error	Program
	47.8b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	17.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (.f64 c b) (*.f64 a d)))))
	27.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	34.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	40.1b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	38.4b	(-.f64 (/.f64 (.f64 c b) (.f64 d d)) (/.f64 a d))
	17.7b	(.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (sqrt.f64 (hypot.f64 d c)))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (*.f64 a d))) (sqrt.f64 (hypot.f64 d c))))
	17.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
	43.0b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
▶	17.1b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	34.2b	(/.f64 b c)

Compiler

Compiled 7551 to 2272 computations (69.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	0.7b	(-.f64 (.f64 c b) (.f64 a d))
	16.1b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series111.0ms (1.3%)

Counts

1 → 48

Calls

1 calls:

111.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 73

Calls

1 calls:

6.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

562×	`times-frac_binary64`
475×	`associate-/l/_binary64`
466×	`associate-/l*_binary64`
465×	`fma-neg_binary64`
359×	`div-sub_binary64`

Counts

121 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	4368
1	439	4066
2	1089	3872
3	4050	3805
4	5223	3805

prune152.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	232	10	242

Error

1.4b

Counts

242 → 10

Alt Table

Status	Error	Program
	17.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
▶	17.2b	(/.f64 (/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c))
	27.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	34.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	40.1b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	38.4b	(-.f64 (/.f64 (.f64 c b) (.f64 d d)) (/.f64 a d))
	43.4b	(/.f64 (-.f64 b (/.f64 (*.f64 a d) c)) (hypot.f64 d c))
	47.8b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	18.0b	(/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (sqrt.f64 (hypot.f64 d c))) (/.f64 (hypot.f64 d c) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (*.f64 a d))) (sqrt.f64 (hypot.f64 d c)))))
	34.2b	(/.f64 b c)

Compiler

Compiled 6393 to 1362 computations (78.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c))
✓	0.2b	(/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (.f64 c b) (.f64 a d))))
	0.7b	(-.f64 (.f64 c b) (.f64 a d))
✓	16.1b	(/.f64 (hypot.f64 d c) (-.f64 (.f64 c b) (.f64 a d)))

series284.0ms (3.5%)

Counts

3 → 144

Calls

3 calls:

111.0ms

(/.f64 (/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (*.f64 c b) (*.f64 a d)))) (hypot.f64 d c))

105.0ms

(/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (*.f64 c b) (*.f64 a d))))

68.0ms

(/.f64 (hypot.f64 d c) (-.f64 (*.f64 c b) (*.f64 a d)))

rewrite87.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

528×	`times-frac_binary64`
254×	`*-un-lft-identity_binary64`
254×	`add-sqr-sqrt_binary64`
254×	`add-cube-cbrt_binary64`
56×	`associate-/l*_binary64`

Counts

3 → 343

Calls

3 calls:

15.0ms

(/.f64 (/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (*.f64 c b) (*.f64 a d)))) (hypot.f64 d c))

6.0ms

(/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (*.f64 c b) (*.f64 a d))))

4.0ms

(/.f64 (hypot.f64 d c) (-.f64 (*.f64 c b) (*.f64 a d)))

simplify417.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

446×	`times-frac_binary64`
367×	`associate-/l*_binary64`
322×	`associate-/r*_binary64`
239×	`associate-/l/_binary64`
229×	`associate-/r/_binary64`

Counts

487 → 595

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	412	18794
1	1184	17414
2	4759	17414
3	5000	17414
4	4981	17414

prune397.0ms (4.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	618	1	619
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	619	10	629

Error

1.4b

Counts

629 → 10

Alt Table

Status	Error	Program
	17.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
✓	17.2b	(/.f64 (/.f64 1 (/.f64 (hypot.f64 d c) (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c))
	47.8b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	17.2b	(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (-.f64 (.f64 b c) (.f64 a d))))
	27.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	34.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	40.1b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	38.4b	(-.f64 (/.f64 (.f64 c b) (.f64 d d)) (/.f64 a d))
	43.4b	(/.f64 (-.f64 b (/.f64 (*.f64 a d) c)) (hypot.f64 d c))
	34.2b	(/.f64 b c)

Compiler

Compiled 21276 to 5549 computations (73.9% saved)

regimes2.2s (26.8%)

Accuracy

Total 10.9b remaining (85.3%)

Threshold costs 0b (0%)

Counts

175 → 5

Compiler

Compiled 20148 to 10934 computations (45.7% saved)

bsearch104.0ms (1.3%)

Steps

Iters	Range		Point
8	3.6702486125626694e+105	2.433852978615785e+109	1.1811328347300783e+108
8	5.6713557182581886e-275	5.710859892421511e-272	4.8471969151433516e-272
10	-3.011750629071687e-95	-4.2312404667478445e-109	-1.2330820875738752e-108
10	-5.731282668638028e+227	-4.7102807471660685e+214	-7.725025339098771e+214

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	100
1	49	100
2	65	100
3	76	100
4	82	100
5	83	100
6	82	100

end133.0ms (1.6%)

Compiler: Compiled 329 to 167 computations (49.2% saved)

Details

analyze1.7s (21%)

sample1.5s (18%)

simplify67.0ms (0.8%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series103.0ms (1.3%)

rewrite11.0ms (0.1%)

simplify91.0ms (1.1%)

prune74.0ms (0.9%)

localize14.0ms (0.2%)

series241.0ms (2.9%)

rewrite33.0ms (0.4%)

simplify129.0ms (1.6%)

prune193.0ms (2.3%)

localize8.0ms (0.1%)

series111.0ms (1.3%)

rewrite17.0ms (0.2%)

simplify120.0ms (1.5%)

prune152.0ms (1.8%)

localize10.0ms (0.1%)

series284.0ms (3.5%)

rewrite87.0ms (1.1%)

simplify417.0ms (5.1%)

prune397.0ms (4.8%)

regimes2.2s (26.8%)

bsearch104.0ms (1.3%)

simplify6.0ms (0.1%)

end133.0ms (1.6%)

Profiling