Details

analyze264.0ms (3.6%)

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)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	124×	body	256	valid
9.0ms	279×	pre	128	true
7.0ms	47×	body	512	valid
4.0ms	85×	body	128	valid
1.0ms	23×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify227.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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: 52.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (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))
24.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite40.0ms (0.6%)

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:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series540.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
135.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
75.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5031	1979

prune101.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.1b

Counts

87 → 3

Compiler

Compiled 2019 to 1194 computations (40.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite59.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
22×	`times-frac_binary64_84`
20×	`*-un-lft-identity_binary64_78`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
11×	`associate-/l*_binary64_23`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
8×	`add-log-exp_binary64_117`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `pow1_binary64_139` `flip3-+_binary64_81`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 99

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series897.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
317.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune161.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Merged error: 0b

Counts

114 → 7

Compiler

Compiled 3273 to 2017 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_78`
15×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`times-frac_binary64_84`
8×	`add-log-exp_binary64_117`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`associate-/r*_binary64_22`
3×	`sqrt-prod_binary64_94` `associate-/l*_binary64_23`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series666.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

355.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
70.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5087	1969

prune115.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Merged error: 0b

Counts

91 → 5

Compiler

Compiled 2340 to 1455 computations (37.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
0.3b	(.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.4b	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 c (.f64 a 4)) 3)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.6b	(pow.f64 (.f64 c (.f64 a 4)) 3)

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_100`
30×	`times-frac_binary64_84` `*-un-lft-identity_binary64_78`
26×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
24×	`difference-of-squares_binary64_47` `pow1_binary64_139`
22×	`add-cube-cbrt_binary64_113`
21×	`sqr-pow_binary64_50`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
10×	`associate-/l*_binary64_23`
9×	`unpow-prod-down_binary64_157`
6×	`associate-*r/_binary64_20`
5×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
4×	`associate-l_binary64_19` `add-log-exp_binary64_117` `distribute-lft-out--_binary64_30` `associate-r_binary64_18`
3×	`rem-cube-cbrt_binary64_101` `pow-exp_binary64_146` `flip-+_binary64_52` `pow-pow_binary64_150` `associate-/r*_binary64_22` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`*-commutative_binary64_9` `associate-/r/_binary64_24` `associate-/l/_binary64_25`
1×	`cube-mult_binary64_108` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `div-sub_binary64_83` `unpow3_binary64_144` `cube-prod_binary64_106`

Counts

4 → 134

Calls

4 calls:

18.0ms	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 c (.f64 a 4)) 3)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
16.0ms	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
10.0ms	(.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
7.0ms	(pow.f64 (.f64 c (.f64 a 4)) 3)

series551.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 c (.f64 a 4)) 3)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
142.0ms	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
106.0ms	(.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
77.0ms	(pow.f64 (.f64 c (.f64 a 4)) 3)

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5010	5901

prune420.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Merged error: 0b

Counts

151 → 5

Compiler

Compiled 7676 to 5231 computations (31.9% saved)

regimes523.0ms (7.1%)

Compiler: Compiled 5180 to 3902 computations (24.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.2s (30.4%)

Algorithm

1×

intervals

Results

358.0ms	3782×	body	256	valid
276.0ms	8811×	pre	128	true
212.0ms	1490×	body	512	valid
135.0ms	2728×	body	128	valid
37.0ms	811×	body	128	nan

Compiler

Compiled 1331 to 1004 computations (24.6% saved)

Details

analyze264.0ms (3.6%)

sample42.0ms (0.6%)

simplify227.0ms (3.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series540.0ms (7.4%)

simplify69.0ms (0.9%)

prune101.0ms (1.4%)

localize16.0ms (0.2%)

rewrite59.0ms (0.8%)

series897.0ms (12.3%)

simplify77.0ms (1.1%)

prune161.0ms (2.2%)

localize12.0ms (0.2%)

rewrite32.0ms (0.4%)

series666.0ms (9.1%)

simplify71.0ms (1%)

prune115.0ms (1.6%)

localize25.0ms (0.3%)

rewrite74.0ms (1%)

series551.0ms (7.5%)

simplify96.0ms (1.3%)

prune420.0ms (5.7%)

regimes523.0ms (7.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (30.4%)

Profiling