Details

analyze447.0ms (6.1%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample21.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune3.0ms (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

38.2b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

35.5b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
35.5b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_17832` `add-log-exp_binary64_17849`
3×	`sqrt-prod_binary64_17826` `*-un-lft-identity_binary64_17810` `add-cube-cbrt_binary64_17845` `pow1_binary64_17871`
2×	`sqrt-div_binary64_17827` `flip-+_binary64_17784` `add-exp-log_binary64_17848` `flip3-+_binary64_17813` `add-cbrt-cube_binary64_17846`
1×	`sum-log_binary64_17901` `sqrt-pow1_binary64_17828` `+-commutative_binary64_17740` `rem-sqrt-square_binary64_17823` `pow1/2_binary64_17890`

Counts

2 → 26

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series355.0ms (4.8%)

Counts

2 → 34

Calls

2 calls:

271.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
84.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1222 to 1069 computations (12.5% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4969	1388
1	4969	1388

prune77.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	53	7	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	8	61

Error

0.9b

Counts

61 → 8

Compiler

Compiled 1189 to 378 computations (68.2% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
35.5b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
35.5b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite59.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`sqrt-prod_binary64_17826`
62×	`add-sqr-sqrt_binary64_17832`
38×	`sqrt-pow1_binary64_17828`
32×	`sqrt-div_binary64_17827`
31×	`pow1_binary64_17871`
20×	`*-un-lft-identity_binary64_17810` `add-cube-cbrt_binary64_17845` `pow1/2_binary64_17890`
15×	`swap-sqr_binary64_17777`
12×	`rem-sqrt-square_binary64_17823`
9×	`unswap-sqr_binary64_17778` `associate-r_binary64_17750` `flip-+_binary64_17784` `flip3-+_binary64_17813` `pow-prod-up_binary64_17880` `associate-l_binary64_17751`
6×	`add-exp-log_binary64_17848` `add-cbrt-cube_binary64_17846`
5×	`pow-prod-down_binary64_17881` `pow-sqr_binary64_17783`
4×	`add-log-exp_binary64_17849` `frac-times_binary64_17820` `sqr-abs_binary64_17825`
2×	`associate-l/_binary64_17753` `associate-r/_binary64_17752`
1×	`cbrt-unprod_binary64_17843` `sqrt-unprod_binary64_17830` `prod-exp_binary64_17859` `*-commutative_binary64_17741` `rem-square-sqrt_binary64_17822` `pow-plus_binary64_17873` `pow2_binary64_17891`

Counts

4 → 138

Calls

8 calls:

22.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
7.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series1.4s (18.5%)

Counts

4 → 89

Calls

4 calls:

435.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
325.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
317.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
293.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))

Compiler

Compiled 5885 to 4720 computations (19.8% saved)

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4984	7037
1	4984	7037

prune226.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	227	8	235

Error

0.9b

Counts

235 → 8

Compiler

Compiled 7486 to 1536 computations (79.5% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms (0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Error

0.9b

Counts

8 → 8

Compiler

Compiled 7 to 17 computations (-142.9% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms (0%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	3	3
Total	8	8

Error

0.9b

Counts

8 → 8

Compiler

Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	112	278
1	112	278

regimes547.0ms (7.4%)

Compiler: Compiled 2581 to 2087 computations (19.1% saved)

bsearch39.0ms (0.5%)

Steps

Iters	Range		Point
9	3.4020336246076314e+55	4.041846273684266e+60	3.9888983964713314e+60
9	-6.770150352934166e+128	-1.1214418978045741e+123	-4.488947755092404e+128

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes518.0ms (7%)

Compiler: Compiled 570 to 734 computations (-28.8% saved)

bsearch51.0ms (0.7%)

Steps

Iters	Range	Point
7	7.816730778774516e-56	3.9821578143401896e-54	3.924969607937373e-54
9	-2.1139305079492734e-51	-9.570372280977877e-57	-2.0053498903303235e-54
9	-6.770150352934166e+128	-1.1214418978045741e+123	-9.605147171149148e+125

Iters

Range

Point

7.816730778774516e-56

3.9821578143401896e-54

3.924969607937373e-54

-2.1139305079492734e-51

-9.570372280977877e-57

-2.0053498903303235e-54

-6.770150352934166e+128

-1.1214418978045741e+123

-9.605147171149148e+125

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes402.0ms (5.4%)

Compiler: Compiled 410 to 594 computations (-44.9% saved)

bsearch77.0ms (1%)

Steps

Iters	Range		Point
8	1.8902397077512067e+102	4.0703330670933297e+105	1.3270625385352505e+103
9	3.4020336246076314e+55	4.041846273684266e+60	1.8714558560145953e+56
8	8.991863200673344e+41	9.269724409635638e+45	9.121051616478697e+45
7	7.816730778774516e-56	3.9821578143401896e-54	4.972173623440741e-55
10	-1.1325315815149874e-06	-3.212428942538539e-17	-1.3722124681143297e-08

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes413.0ms (5.6%)

Compiler: Compiled 213 to 344 computations (-61.5% saved)

bsearch175.0ms (2.4%)

Steps

Iters	Range		Point
8	1.8902397077512067e+102	4.0703330670933297e+105	1.914489363399924e+102
8	4.041846273684266e+60	1.3879685563450334e+64	1.6249162523000812e+62
8	8.991863200673344e+41	9.269724409635638e+45	1.1995838869215986e+45
7	7.816730778774516e-56	3.9821578143401896e-54	8.72782298761248e-56
8	1.7496911419096126e-233	4.601084994951012e-229	2.304809989723087e-232
6	5.540469225236547e-239	2.351237806688917e-238	1.2545824004578874e-238
5	9.727320119207529e-252	2.799179565772394e-251	1.1148972220753654e-251
8	9.0051446542674e-296	1.0203144772550947e-292	7.366192176249098e-295
7	9.426957439201869e-303	1.3414586710205054e-300	4.667908854129587e-302
8	-8.368461280858123e-251	-1.0362328385380879e-253	-1.9719397252834922e-253
9	-2.2900983615724997e-164	-8.184125480246413e-170	-5.59135491821388e-165
7	-8.505502733602698e-151	-2.293232988481832e-152	-3.15728364052437e-151
8	-1.7676297994812707e-37	-3.082628203080835e-42	-3.242442730210987e-38

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes222.0ms (3%)

Compiler: Compiled 42 to 117 computations (-178.6% saved)

bsearch93.0ms (1.3%)

Steps

Iters	Range		Point
7	7.816730778774516e-56	3.9821578143401896e-54	7.708158259094176e-55
8	9.0051446542674e-296	1.0203144772550947e-292	2.631032794434887e-293
7	9.426957439201869e-303	1.3414586710205054e-300	2.845999638125896e-301
8	-8.368461280858123e-251	-1.0362328385380879e-253	-5.939447749900448e-252
9	-2.2900983615724997e-164	-8.184125480246413e-170	-3.710561020036677e-166
7	-8.505502733602698e-151	-2.293232988481832e-152	-3.803174774874433e-152
8	-1.7676297994812707e-37	-3.082628203080835e-42	-3.0972918864632994e-38

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes182.0ms (2.5%)

Compiler: Compiled 36 to 105 computations (-191.7% saved)

bsearch126.0ms (1.7%)

Steps

Iters	Range		Point
8	1.8902397077512067e+102	4.0703330670933297e+105	1.914489363399924e+102
8	4.041846273684266e+60	1.3879685563450334e+64	6.033133859087058e+63
8	8.991863200673344e+41	9.269724409635638e+45	2.755993599020533e+45
7	7.816730778774516e-56	3.9821578143401896e-54	2.0094051567064338e-54
8	1.0203144772550947e-292	7.337639196260526e-290	1.4071564533574446e-292
8	-1.6359208114423576e-239	-7.121286243318625e-244	-9.583503801657816e-240
9	-2.2900983615724997e-164	-8.184125480246413e-170	-7.213598741186633e-169
7	-8.505502733602698e-151	-2.293232988481832e-152	-5.0156735314691095e-151
8	-1.7676297994812707e-37	-3.082628203080835e-42	-8.764735511337867e-40

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes129.0ms (1.7%)

Compiler: Compiled 30 to 93 computations (-210% saved)

bsearch29.0ms (0.4%)

Steps

Iters	Range		Point
10	1.5646229661712345e-89	1.1918602184717537e-78	7.5331716743775265e-81
7	-1.2543136394081815e-49	-2.6482419491630694e-51	-1.1331570714098637e-50

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes115.0ms (1.6%)

Compiler: Compiled 24 to 81 computations (-237.5% saved)

bsearch107.0ms (1.4%)

Steps

Iters	Range		Point
8	1.8902397077512067e+102	4.0703330670933297e+105	1.914489363399924e+102
9	3.4020336246076314e+55	4.041846273684266e+60	3.7771068876195965e+60
8	8.991863200673344e+41	9.269724409635638e+45	9.121051616478697e+45
10	1.5646229661712345e-89	1.1918602184717537e-78	1.9217162317999586e-84
6	5.540469225236547e-239	2.351237806688917e-238	1.7750825613497865e-238
8	-1.6359208114423576e-239	-7.121286243318625e-244	-4.2035523502443245e-240
7	-4.3633666759512576e-172	-1.7526372124763143e-174	-2.4256580704478053e-174
8	-170.40489543807897	-0.24049053961890762	-3.82205946405465

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes73.0ms (1%)

Compiler: Compiled 21 to 72 computations (-242.9% saved)

bsearch18.0ms (0.2%)

Steps

Iters	Range		Point
10	1.5646229661712345e-89	1.1918602184717537e-78	3.380560913491828e-79

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes34.0ms (0.5%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch13.0ms (0.2%)

Steps

Iters	Range		Point
7	1.3038577455954245e-222	2.6190240942509686e-220	2.5665030622105744e-220

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0.4%)

Accuracy

Total 24.9b remaining (98%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch13.0ms (0.2%)

Compiler: Compiled 330 to 225 computations (31.8% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	192	475
1	192	475

end0.0ms (0%)

sample1.1s (14.6%)

Algorithm

1×

intervals

Results

293.0ms

8000×

body

128

valid

Compiler

Compiled 553 to 404 computations (26.9% saved)

Pareto

0.3841562633281757

Details

analyze447.0ms (6.1%)

sample21.0ms (0.3%)

simplify100.0ms (1.3%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite14.0ms (0.2%)

series355.0ms (4.8%)

simplify74.0ms (1%)

prune77.0ms (1%)

localize12.0ms (0.2%)

rewrite59.0ms (0.8%)

series1.4s (18.5%)

simplify102.0ms (1.4%)

prune226.0ms (3.1%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

regimes547.0ms (7.4%)

bsearch39.0ms (0.5%)

regimes518.0ms (7%)

bsearch51.0ms (0.7%)

regimes402.0ms (5.4%)

bsearch77.0ms (1%)

regimes413.0ms (5.6%)

bsearch175.0ms (2.4%)

regimes222.0ms (3%)

bsearch93.0ms (1.3%)

regimes182.0ms (2.5%)

bsearch126.0ms (1.7%)

regimes129.0ms (1.7%)

bsearch29.0ms (0.4%)

regimes115.0ms (1.6%)

bsearch107.0ms (1.4%)

regimes73.0ms (1%)

bsearch18.0ms (0.2%)

regimes34.0ms (0.5%)

bsearch13.0ms (0.2%)

regimes27.0ms (0.4%)

bsearch13.0ms (0.2%)

simplify11.0ms (0.2%)

end0.0ms (0%)

sample1.1s (14.6%)

Profiling