Details

analyze272.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample45.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	123×	body	256	valid
9.0ms	286×	pre	128	true
6.0ms	44×	body	512	valid
4.0ms	89×	body	128	valid
1.0ms	30×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify389.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (301.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 52.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
27.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
6×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`pow1_binary64_139`
4×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
3×	`distribute-lft-out--_binary64_30`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `diff-log_binary64_170` `sqrt-div_binary64_95` `associate-/l/_binary64_25` `sub-neg_binary64_71`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `pow1/2_binary64_158`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series252.0ms (3.8%)

Counts

4 → 36

Calls

4 calls:

108.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
69.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
47.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
27.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5191	2693

prune151.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 0.8b

Counts

111 → 9

Compiler

Compiled 2828 to 1592 computations (43.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(+.f64 (/.f64 c b) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
0.3b	(.f64 a (.f64 c c))
0.3b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_116`
17×	`add-cbrt-cube_binary64_114`
12×	`prod-exp_binary64_127` `times-frac_binary64_84` `associate-/r_binary64_22` `-un-lft-identity_binary64_78`
11×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113`
9×	`div-exp_binary64_129`
8×	`pow1_binary64_139`
6×	`cbrt-unprod_binary64_111` `unpow-prod-down_binary64_157` `cube-prod_binary64_106`
5×	`add-log-exp_binary64_117`
3×	`associate-l_binary64_19` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `pow-prod-down_binary64_149`
2×	`cube-mult_binary64_108` `sqr-pow_binary64_50` `unpow3_binary64_144`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `frac-add_binary64_86` `flip-+_binary64_52` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-r_binary64_18` `associate-/l_binary64_23` `unswap-sqr_binary64_46` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

3 → 79

Calls

3 calls:

16.0ms	(+.f64 (/.f64 c b) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
8.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
5.0ms	(.f64 a (.f64 c c))

series247.0ms (3.7%)

Counts

3 → 24

Calls

3 calls:

159.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
49.0ms	(+.f64 (/.f64 c b) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
39.0ms	(.f64 a (.f64 c c))

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4978	1519
1	4978	1519

prune97.0ms (1.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	98	14	112

Merged error: 0.7b

Counts

112 → 14

Compiler

Compiled 2181 to 975 computations (55.3% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 a a) (pow.f64 b 6)) (pow.f64 c 4))
0.5b	(.f64 (/.f64 c b) (-.f64 (/.f64 c b) (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3))))
0.6b	(pow.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) 3)
0.7b	(pow.f64 (/.f64 c b) 3)

rewrite91.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`times-frac_binary64_84` `add-exp-log_binary64_116`
76×	`add-sqr-sqrt_binary64_100`
54×	`unpow-prod-down_binary64_157`
51×	`*-un-lft-identity_binary64_78`
49×	`add-cube-cbrt_binary64_113`
41×	`prod-exp_binary64_127` `cube-prod_binary64_106`
32×	`cancel-sign-sub-inv_binary64_44`
31×	`add-cbrt-cube_binary64_114`
29×	`div-exp_binary64_129`
28×	`pow-exp_binary64_146`
24×	`associate-l_binary64_19`
18×	`pow-to-exp_binary64_147`
17×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
15×	`sqr-pow_binary64_50`
14×	`unswap-sqr_binary64_46`
13×	`associate-r_binary64_18`
9×	`cbrt-unprod_binary64_111`
8×	`div-inv_binary64_75` `pow1_binary64_139`
7×	`cbrt-undiv_binary64_112`
6×	`rem-cube-cbrt_binary64_101` `cube-mult_binary64_108` `pow-unpow_binary64_155` `unpow3_binary64_144`
4×	`add-log-exp_binary64_117`
3×	`frac-times_binary64_88` `associate-*r/_binary64_20`
2×	`-commutative_binary64_9` `cube-div_binary64_107` `frac-sub_binary64_87` `flip3--_binary64_82` `pow-pow_binary64_150` `flip--_binary64_53` `associate-l/_binary64_21` `difference-of-squares_binary64_47` `sub-neg_binary64_71`
1×	`distribute-lft-out--_binary64_30` `pow-prod-down_binary64_149`

Counts

4 → 246

Calls

4 calls:

25.0ms	(.f64 (/.f64 c b) (-.f64 (/.f64 c b) (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3))))
11.0ms	(.f64 (/.f64 (.f64 a a) (pow.f64 b 6)) (pow.f64 c 4))
10.0ms	(pow.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) 3)
5.0ms	(pow.f64 (/.f64 c b) 3)

series613.0ms (9.1%)

Counts

4 → 33

Calls

4 calls:

235.0ms	(pow.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) 3)
223.0ms	(.f64 (/.f64 (.f64 a a) (pow.f64 b 6)) (pow.f64 c 4))
83.0ms	(.f64 (/.f64 c b) (-.f64 (/.f64 c b) (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3))))
72.0ms	(pow.f64 (/.f64 c b) 3)

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5239	5429

prune706.0ms (10.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	278	15	293

Merged error: 0.7b

Counts

293 → 15

Compiler

Compiled 15130 to 7327 computations (51.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)))) (.f64 a 2))
0.3b	(/.f64 (*.f64 a c) b)
0.3b	(.f64 (.f64 a a) (*.f64 c c))
0.3b	(/.f64 (.f64 (.f64 a a) (*.f64 c c)) (pow.f64 b 3))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-exp-log_binary64_116`
51×	`add-cbrt-cube_binary64_114`
37×	`prod-exp_binary64_127`
32×	`pow1_binary64_139`
21×	`cbrt-unprod_binary64_111` `div-exp_binary64_129`
16×	`times-frac_binary64_84` `associate-/r*_binary64_22`
14×	`pow-prod-down_binary64_149`
12×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`cbrt-undiv_binary64_112`
6×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
5×	`pow-exp_binary64_146` `pow-to-exp_binary64_147`
4×	`add-log-exp_binary64_117` `pow-prod-up_binary64_148` `pow-plus_binary64_141`
3×	`frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-r/_binary64_20` `clear-num_binary64_77` `associate-/l/_binary64_25`
2×	`cube-mult_binary64_108` `pow2_binary64_159` `pow-sqr_binary64_51` `sqr-pow_binary64_50` `unpow3_binary64_144`
1×	`-commutative_binary64_9` `associate-l_binary64_19` `frac-add_binary64_86` `flip-+_binary64_52` `associate-r*_binary64_18` `unswap-sqr_binary64_46` `flip3-+_binary64_81`

Counts

4 → 129

Calls

4 calls:

17.0ms	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)))) (.f64 a 2))
13.0ms	(/.f64 (.f64 (.f64 a a) (*.f64 c c)) (pow.f64 b 3))
8.0ms	(.f64 (.f64 a a) (*.f64 c c))
4.0ms	(/.f64 (*.f64 a c) b)

series388.0ms (5.8%)

Counts

4 → 33

Calls

4 calls:

175.0ms	(/.f64 (.f64 (.f64 a a) (*.f64 c c)) (pow.f64 b 3))
84.0ms	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)))) (.f64 a 2))
76.0ms	(/.f64 (*.f64 a c) b)
52.0ms	(.f64 (.f64 a a) (*.f64 c c))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5212	2567

prune155.0ms (2.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	162	15	177

Merged error: 0.7b

Counts

177 → 15

Compiler

Compiled 4022 to 1719 computations (57.3% saved)

regimes409.0ms (6.1%)

Compiler: Compiled 5924 to 4198 computations (29.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	21
1	69	21

end0.0ms (0%)

sample2.4s (35.9%)

Algorithm

1×

intervals

Results

379.0ms	3849×	body	256	valid
280.0ms	8856×	pre	128	true
212.0ms	1459×	body	512	valid
134.0ms	2692×	body	128	valid
41.0ms	856×	body	128	nan

Compiler

Compiled 1515 to 1076 computations (29% saved)

Details

analyze272.0ms (4.1%)

sample45.0ms (0.7%)

simplify389.0ms (5.8%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite33.0ms (0.5%)

series252.0ms (3.8%)

simplify68.0ms (1%)

prune151.0ms (2.3%)

localize12.0ms (0.2%)

rewrite35.0ms (0.5%)

series247.0ms (3.7%)

simplify41.0ms (0.6%)

prune97.0ms (1.4%)

localize27.0ms (0.4%)

rewrite91.0ms (1.4%)

series613.0ms (9.1%)

simplify99.0ms (1.5%)

prune706.0ms (10.5%)

localize17.0ms (0.3%)

rewrite56.0ms (0.8%)

series388.0ms (5.8%)

simplify75.0ms (1.1%)

prune155.0ms (2.3%)

regimes409.0ms (6.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.4s (35.9%)

Profiling