Details

analyze13.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify272.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (173.0ms)

Iter	Nodes	Cost
0	4979	22
1	4979	22

prune2.0ms (0.1%)

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

22.1b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

21.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
21.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_707`
7×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
4×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-log-exp_binary64_799` `frac-times_binary64_770` `add-sqr-sqrt_binary64_782`
3×	`associate-/r*_binary64_704` `times-frac_binary64_766` `flip--_binary64_735` `flip3--_binary64_764`
2×	`cbrt-undiv_binary64_794` `associate-l/_binary64_703` `associate-/r/_binary64_706` `associate-r/_binary64_702` `div-exp_binary64_811` `pow1_binary64_821`
1×	`frac-2neg_binary64_771` `prod-exp_binary64_809` `div-inv_binary64_757` `associate-/l*_binary64_705` `+-commutative_binary64_690` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `clear-num_binary64_759`

Counts

2 → 42

Calls

4 calls:

12.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series199.0ms (5%)

Counts

2 → 24

Calls

2 calls:

113.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
86.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 444 to 378 computations (14.9% saved)

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5237	1122

prune62.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	4	67

Error

0.4b

Counts

67 → 4

Compiler

Compiled 1255 to 240 computations (80.9% saved)

localize12.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
0.0b	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
21.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
21.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite81.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64_782`
93×	`*-un-lft-identity_binary64_760`
90×	`times-frac_binary64_766`
55×	`add-cube-cbrt_binary64_795`
54×	`sqrt-prod_binary64_776`
36×	`associate-l_binary64_701`
30×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
13×	`distribute-lft-out_binary64_711`
10×	`sqrt-div_binary64_777`
9×	`unswap-sqr_binary64_728`
8×	`pow1_binary64_821`
6×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/r*_binary64_704` `difference-of-squares_binary64_729` `flip-+_binary64_734` `distribute-lft-out--_binary64_712`
5×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
4×	`prod-exp_binary64_809` `add-log-exp_binary64_799` `associate-/l*_binary64_705` `cbrt-unprod_binary64_793`
3×	`div-inv_binary64_757`
2×	`rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `frac-times_binary64_770` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 175

Calls

8 calls:

36.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
9.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series429.0ms (10.7%)

Counts

4 → 64

Calls

4 calls:

111.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
111.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
109.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
97.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 2062 to 1484 computations (28% saved)

simplify108.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5167	6500

prune202.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Error

0.4b

Counts

243 → 5

Compiler

Compiled 7654 to 885 computations (88.4% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

21.8b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
0.0b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
21.8b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))

rewrite46.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64_766`
64×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
22×	`associate-/r*_binary64_704`
17×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729`
11×	`associate-/r/_binary64_706` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799` `div-exp_binary64_811`
6×	`div-inv_binary64_757` `associate-/l*_binary64_705` `flip--_binary64_735` `flip3--_binary64_764`
5×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794`
2×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804`
1×	`diff-log_binary64_852` `cancel-sign-sub-inv_binary64_726` `inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753` `pow-flip_binary64_834`

Counts

4 → 155

Calls

8 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
9.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(-.f64 (.f64 x x) (.f64 y y))

series386.0ms (9.7%)

Counts

4 → 48

Calls

4 calls:

105.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
101.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
95.0ms	(-.f64 (.f64 x x) (.f64 y y))
84.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1008 to 876 computations (13.1% saved)

simplify93.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4998	5514
1	4998	5514

prune152.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	203	5	208

Error

0.4b

Counts

208 → 5

Compiler

Compiled 4959 to 850 computations (82.9% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Error

0.4b

Counts

5 → 5

Compiler

Compiled 0 to 0 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	115	231
1	115	231

regimes115.0ms (2.9%)

Compiler: Compiled 505 to 308 computations (39% saved)

bsearch63.0ms (1.6%)

Steps

Iters	Range		Point
8	3.656656245399415e-174	2.3344116858421214e-169	2.2931306999859318e-169
7	-1.6682272233496304e-172	-5.901696694702968e-174	-1.0294507382078244e-172
8	-4.080102610617992e-162	-1.5737736075632083e-166	-9.049599147467105e-163
9	-2.9296370381706477e+157	-1.9829149111454482e+151	-1.3513757347195584e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes76.0ms (1.9%)

Compiler: Compiled 136 to 114 computations (16.2% saved)

bsearch60.0ms (1.5%)

Steps

Iters	Range		Point
8	3.656656245399415e-174	2.3344116858421214e-169	2.2931306999859318e-169
7	-1.6682272233496304e-172	-5.901696694702968e-174	-2.8180354867586467e-173
8	-4.080102610617992e-162	-1.5737736075632083e-166	-1.0488401738504467e-164
8	-1.1597459988930132e-30	-2.6154204945027845e-34	-1.14108427891841e-30

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes77.0ms (1.9%)

Compiler: Compiled 106 to 96 computations (9.4% saved)

bsearch61.0ms (1.5%)

Steps

Iters	Range		Point
9	9.8866015244286e-167	1.6233853915482778e-158	1.5712870211415494e-162
7	-1.6682272233496304e-172	-5.901696694702968e-174	-1.2247246025880804e-172
8	-4.080102610617992e-162	-1.5737736075632083e-166	-3.3476235632622506e-164
8	-1.1597459988930132e-30	-2.6154204945027845e-34	-1.14108427891841e-30

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes76.0ms (1.9%)

Compiler: Compiled 76 to 78 computations (-2.6% saved)

bsearch37.0ms (0.9%)

Steps

Iters	Range		Point
7	4.6412505681786215e-125	1.135415275937066e-123	2.4978925429798098e-124
11	-3.123873915030774e-124	-1.1748320775319972e-147	-3.9751550003611877e-146

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes73.0ms (1.8%)

Compiler: Compiled 54 to 62 computations (-14.8% saved)

bsearch32.0ms (0.8%)

Steps

Iters	Range		Point
7	4.6412505681786215e-125	1.135415275937066e-123	7.73441976440763e-124
11	-3.123873915030774e-124	-1.1748320775319972e-147	-1.3932628819163734e-141

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes61.0ms (1.5%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch26.0ms (0.6%)

Steps

Iters	Range		Point
7	4.6412505681786215e-125	1.135415275937066e-123	4.6831456259906935e-125
7	-1.6682272233496304e-172	-5.901696694702968e-174	-2.573943156283327e-173

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes13.0ms (0.3%)

Accuracy

Total 4.3b remaining (92%)

Threshold costs 0b (0%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch9.0ms (0.2%)

Compiler: Compiled 261 to 146 computations (44.1% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	128	351
1	128	351

end0.0ms (0%)

sample1.0s (25.8%)

Algorithm

1×

intervals

Results

314.0ms	8000×	body	128	valid
165.0ms	8000×	pre	128	true

Compiler

Compiled 457 to 273 computations (40.3% saved)

Pareto

0.5287794841252277

Details

analyze13.0ms (0.3%)

sample24.0ms (0.6%)

simplify272.0ms (6.8%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite20.0ms (0.5%)

series199.0ms (5%)

simplify40.0ms (1%)

prune62.0ms (1.6%)

localize12.0ms (0.3%)

rewrite81.0ms (2%)

series429.0ms (10.7%)

simplify108.0ms (2.7%)

prune202.0ms (5.1%)

localize11.0ms (0.3%)

rewrite46.0ms (1.2%)

series386.0ms (9.7%)

simplify93.0ms (2.3%)

prune152.0ms (3.8%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.2%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

regimes115.0ms (2.9%)

bsearch63.0ms (1.6%)

regimes76.0ms (1.9%)

bsearch60.0ms (1.5%)

regimes77.0ms (1.9%)

bsearch61.0ms (1.5%)

regimes76.0ms (1.9%)

bsearch37.0ms (0.9%)

regimes73.0ms (1.8%)

bsearch32.0ms (0.8%)

regimes61.0ms (1.5%)

bsearch26.0ms (0.6%)

regimes13.0ms (0.3%)

bsearch9.0ms (0.2%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample1.0s (25.8%)

Profiling