Details

analyze968.0ms (2.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5644	164
0	3	3
1	3	3

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
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample60.0ms (0.2%)

Algorithm

1×

intervals

Results

12.0ms	173×	body	128	valid
9.0ms	35×	body	1024	valid
6.0ms	34×	body	512	valid
6.0ms	23×	body	1024	nan
4.0ms	52×	body	128	nan
3.0ms	14×	body	512	nan
2.0ms	13×	body	256	valid
1.0ms	7×	body	256	nan
0.0ms	1×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify69.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5192	41

prune4.0ms (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

42.6b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize166.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
12.2b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite351.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

42.5b

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117` `associate-l_binary64_19` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `associate-r_binary64_18`
2×	`associate--l+_binary64_15` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `sub-neg_binary64_71` `cancel-sign-sub-inv_binary64_44` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `pow-prod-down_binary64_149` `-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`

Counts

4 → 80

Calls

4 calls:

19.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
15.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
14.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series5.8s (17%)

Error

6.2b

Counts

4 → 61

Calls

4 calls:

2.7s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
1.7s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
1.1s	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
45.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 11120 to 9244 computations (16.9% saved)

simplify94.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4966	7161
1	4966	7161

prune385.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	133	8	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Error

6.2b

Counts

142 → 8

Compiler

Compiled 6492 to 4064 computations (37.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.5b	(/.f64 (*.f64 t t) x)
13.5b	(/.f64 (.f64 l l) (.f64 x x))
18.0b	(/.f64 (.f64 t t) (.f64 x x))
27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite258.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

33×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`associate-*r/_binary64_20`
16×	`frac-add_binary64_86`
10×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
9×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `flip3-+_binary64_81` `flip-+_binary64_52` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`

Counts

4 → 86

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
7.0ms	(/.f64 (.f64 l l) (.f64 x x))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5815 to 1665 computations (71.4% saved)

series1.9s (5.4%)

Error

0.4b

Counts

4 → 40

Calls

4 calls:

1.4s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
135.0ms	(/.f64 (.f64 t t) (.f64 x x))
123.0ms	(/.f64 (.f64 l l) (.f64 x x))
102.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 7299 to 5544 computations (24% saved)

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5056	5181

prune330.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	125	9	134

Error

0.4b

Counts

134 → 9

Compiler

Compiled 7376 to 2922 computations (60.4% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

18.0b	(/.f64 (.f64 t t) (.f64 x x))
18.0b	(/.f64 (.f64 t t) (.f64 x x))
27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite454.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

40×	`associate-*r/_binary64_20`
32×	`frac-add_binary64_86`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`sqrt-div_binary64_95`
14×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`add-sqr-sqrt_binary64_100` `prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111`
6×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `sqrt-prod_binary64_94` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 88

Calls

4 calls:

19.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
19.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 11120 to 2892 computations (74% saved)

series4.6s (13.5%)

Error

0.4b

Counts

4 → 60

Calls

4 calls:

2.0s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
2.0s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
145.0ms	(/.f64 (.f64 t t) (.f64 x x))
144.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 20624 to 14248 computations (30.9% saved)

simplify103.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4996	10356
1	4996	10356

prune720.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	147	10	157

Error

0.4b

Counts

157 → 10

Compiler

Compiled 16338 to 6176 computations (62.2% saved)

localize50.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
27.5b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite917.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

80×	`associate-*r/_binary64_20`
64×	`frac-add_binary64_86`
40×	`sqrt-div_binary64_95`
28×	`flip3-+_binary64_81` `flip-+_binary64_52`
12×	`add-sqr-sqrt_binary64_100` `sqrt-prod_binary64_94`
8×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`

Counts

4 → 92

Calls

4 calls:

22.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
20.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
19.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
18.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

Compiler

Compiled 22060 to 5568 computations (74.8% saved)

series9.4s (27.6%)

Error

0.4b

Counts

4 → 96

Calls

4 calls:

2.1s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
2.1s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
2.1s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
2.1s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

Compiler

Compiled 53668 to 30918 computations (42.4% saved)

simplify184.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5018	19624

prune1.9s (5.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	187	11	198

Error

0.4b

Counts

198 → 11

Compiler

Compiled 37736 to 13164 computations (65.1% saved)

regimes2.7s (7.8%)

Accuracy

Total 10.6b remaining (94.8%)

Threshold costs 0b (0%)

Compiler

Compiled 35203 to 21170 computations (39.9% saved)

bsearch349.0ms (1%)

Steps

Iters	Range		Point
5	4.605607333087785e-58	9.939440791194558e-58	9.828494013545358e-58
9	1.1008903000418713e-163	3.48692481349849e-156	1.1177883439917205e-163
5	1.23208751801357e-245	3.4660229240829674e-245	3.421764604155924e-245
7	-1.1085945162158009e+75	-1.698324069289011e+73	-5.1596595017542885e+73

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	238
1	116	238

end6.0ms (0%)

Compiler: Compiled 156 to 100 computations (35.9% saved)

sample2.2s (6.5%)

Algorithm

1×

intervals

Results

360.0ms	5332×	body	128	valid
319.0ms	1207×	body	1024	valid
201.0ms	770×	body	1024	nan
183.0ms	883×	body	512	valid
101.0ms	507×	body	512	nan
98.0ms	1486×	body	128	nan
67.0ms	510×	body	256	valid
36.0ms	285×	body	256	nan
23.0ms	68×	body	2048	valid

Compiler

Compiled 921 to 461 computations (49.9% saved)

Details

analyze968.0ms (2.8%)

sample60.0ms (0.2%)

simplify69.0ms (0.2%)

prune4.0ms (0%)

localize166.0ms (0.5%)

rewrite351.0ms (1%)

series5.8s (17%)

simplify94.0ms (0.3%)

prune385.0ms (1.1%)

localize25.0ms (0.1%)

rewrite258.0ms (0.8%)

series1.9s (5.4%)

simplify60.0ms (0.2%)

prune330.0ms (1%)

localize35.0ms (0.1%)

rewrite454.0ms (1.3%)

series4.6s (13.5%)

simplify103.0ms (0.3%)

prune720.0ms (2.1%)

localize50.0ms (0.1%)

rewrite917.0ms (2.7%)

series9.4s (27.6%)

simplify184.0ms (0.5%)

prune1.9s (5.6%)

regimes2.7s (7.8%)

bsearch349.0ms (1%)

simplify4.0ms (0%)

end6.0ms (0%)

sample2.2s (6.5%)

Profiling