Details

analyze5.1s

Algorithm

Search

True	Other	False	Iter
0%	99.2%	0.8%	0
0%	99.2%	0.8%	1
0%	99.2%	0.8%	2
0%	99.2%	0.8%	3
0%	99.2%	0.8%	4
0%	99.2%	0.8%	5
0%	99.2%	0.8%	6
0%	99.2%	0.8%	7
0%	99.2%	0.8%	8
0%	99.2%	0.8%	9
0%	99.2%	0.8%	10
0%	99.2%	0.8%	11
0%	99.2%	0.8%	12
0%	99.2%	0.8%	13
0%	99.2%	0.8%	14

sample723.0ms

Algorithm

intervals

Results

403.0ms	1758×	body	80	invalid
65.0ms	256×	body	80	valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5356	142

prune29.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.8b

Counts

2 → 1

localize104.0ms

Local error

Found 4 expressions with local error:

8.7b	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.7b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
10.9b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`flip3--_binary64_5067` `flip--_binary64_5094`
20×	`add-sqr-sqrt_binary64_5053`
16×	`frac-times_binary64_5060`
12×	`add-cbrt-cube_binary64_5040` `-un-lft-identity_binary64_5068` `associate-l_binary64_5128` `pow1_binary64_5014` `associate-r*_binary64_5127` `add-exp-log_binary64_5032` `add-cube-cbrt_binary64_5039`
8×	`associate-l/_binary64_5130` `associate-r/_binary64_5129` `sub-neg_binary64_5072`
4×	`pow-prod-down_binary64_4995` `distribute-lft-in_binary64_5110` `add-log-exp_binary64_5033` `prod-exp_binary64_5019` `unswap-sqr_binary64_5096` `distribute-rgt-in_binary64_5111` `cbrt-unprod_binary64_5037` `*-commutative_binary64_5136`

Counts

4 → 112

Calls

4 calls:

10.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
9.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
10.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
10.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
201.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
204.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
209.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

simplify87.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5292	4158

prune792.0ms

Filtered

106 candidates to 124 candidates (-17.0%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	105	19	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	19	125

Merged error: 21.1b

Counts

125 → 19

localize113.0ms

Local error

Found 4 expressions with local error:

8.2b	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
8.7b	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.7b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

24×	`flip3--_binary64_5067` `flip--_binary64_5094`
20×	`add-sqr-sqrt_binary64_5053`
16×	`frac-times_binary64_5060`
12×	`add-cbrt-cube_binary64_5040` `-un-lft-identity_binary64_5068` `associate-l_binary64_5128` `pow1_binary64_5014` `associate-r*_binary64_5127` `add-exp-log_binary64_5032` `add-cube-cbrt_binary64_5039`
8×	`associate-l/_binary64_5130` `associate-r/_binary64_5129` `sub-neg_binary64_5072`
4×	`pow-prod-down_binary64_4995` `distribute-lft-in_binary64_5110` `add-log-exp_binary64_5033` `prod-exp_binary64_5019` `unswap-sqr_binary64_5096` `distribute-rgt-in_binary64_5111` `cbrt-unprod_binary64_5037` `*-commutative_binary64_5136`

Counts

4 → 112

Calls

4 calls:

14.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
10.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
9.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
10.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
204.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
202.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
243.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5289	4158

prune828.0ms

Filtered

106 candidates to 124 candidates (-17.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	120	23	143

Merged error: 20.1b

Counts

143 → 23

localize117.0ms

Local error

Found 4 expressions with local error:

9.7b	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
9.7b	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
9.7b	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
10.9b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`flip3--_binary64_5067` `flip--_binary64_5094`
20×	`add-sqr-sqrt_binary64_5053`
16×	`frac-times_binary64_5060`
12×	`add-cbrt-cube_binary64_5040` `-un-lft-identity_binary64_5068` `associate-l_binary64_5128` `pow1_binary64_5014` `associate-r*_binary64_5127` `add-exp-log_binary64_5032` `add-cube-cbrt_binary64_5039`
8×	`associate-l/_binary64_5130` `associate-r/_binary64_5129` `sub-neg_binary64_5072`
4×	`pow-prod-down_binary64_4995` `distribute-lft-in_binary64_5110` `add-log-exp_binary64_5033` `prod-exp_binary64_5019` `unswap-sqr_binary64_5096` `distribute-rgt-in_binary64_5111` `cbrt-unprod_binary64_5037` `*-commutative_binary64_5136`

Counts

4 → 112

Calls

4 calls:

16.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
12.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
11.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
11.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
207.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
202.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
205.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

simplify97.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5232	4116

prune1.1s

Filtered

104 candidates to 124 candidates (-19.2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	1	21	22
Picked	1	0	1
Done	0	0	0
Total	123	24	147

Merged error: 19.4b

Counts

147 → 24

localize141.0ms

Local error

Found 4 expressions with local error:

9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.7b	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
9.7b	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
10.9b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

24×	`flip3--_binary64_5067` `flip--_binary64_5094`
20×	`add-sqr-sqrt_binary64_5053`
16×	`frac-times_binary64_5060`
12×	`add-cbrt-cube_binary64_5040` `-un-lft-identity_binary64_5068` `associate-l_binary64_5128` `pow1_binary64_5014` `associate-r*_binary64_5127` `add-exp-log_binary64_5032` `add-cube-cbrt_binary64_5039`
8×	`associate-l/_binary64_5130` `associate-r/_binary64_5129` `sub-neg_binary64_5072`
4×	`pow-prod-down_binary64_4995` `distribute-lft-in_binary64_5110` `add-log-exp_binary64_5033` `prod-exp_binary64_5019` `unswap-sqr_binary64_5096` `distribute-rgt-in_binary64_5111` `cbrt-unprod_binary64_5037` `*-commutative_binary64_5136`

Counts

4 → 112

Calls

4 calls:

11.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
11.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
11.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
10.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

series810.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
203.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
202.0ms	(.f64 (-.f64 (.f64 y0 b) (.f64 y1 i)) (-.f64 (.f64 x j) (*.f64 z k)))
203.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5066	4122

prune556.0ms

Filtered

105 candidates to 124 candidates (-18.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	123	25	148

Merged error: 19.2b

Counts

148 → 25

regimes8.2s

Accuracy

-19% (11.5b remaining)

Error of 29.1b against oracle of 17.6b and baseline of 27.3b

bsearch1.2s

Steps

Iters	Range		Point
3	1524436884574693/262144	8007875569071879/1048576	6384527728.9537115
8	6083934940218203/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896	3472695741785973/50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237978846405428549423569451580654251209705071092879576217840034217957579701248029256805705844583825408	2.8060144722384305e-223
8	-2701238802204605/1480596630383213935040454376661779933220754639736839877261211431528140022932412039118650826290747144651878100106364319997951107067217649833149230265656644000248389221211290269422784124023054547143233298486439198256390425542656	-1410489955292343/758065474756205534740712640850831325809026375545262017157740252942407691741394964028749223060862538061761587254458531838950966818415436714572405896016201728127175281260180617944465471499803928137335448825056869507271897877839872	-3.5148838574756127e-211
4	-1205244723346137/5070602400912917605986812821504	-4959595773787621/40564819207303340847894502572032	-1.7942870202176659e-16

simplify107.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	2772	884
1	2772	884

end0.0ms

sample25.1s

Algorithm

intervals

Results

14.9s	64513×	body	80	invalid
1.8s	8000×	body	80	valid

Details

analyze5.1s

sample723.0ms

simplify32.0ms

prune29.0ms

localize104.0ms

rewrite44.0ms

series815.0ms

simplify87.0ms

prune792.0ms

localize113.0ms

rewrite47.0ms

series853.0ms

simplify92.0ms

prune828.0ms

localize117.0ms

rewrite54.0ms

series822.0ms

simplify97.0ms

prune1.1s

localize141.0ms

rewrite47.0ms

series810.0ms

simplify77.0ms

prune556.0ms

regimes8.2s

bsearch1.2s

simplify107.0ms

end0.0ms

sample25.1s

Profiling