Details

analyze2.2s

Algorithm

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
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample138.0ms

Algorithm

intervals

Results

64.0ms	80×	body	1280	valid
23.0ms	42×	body	640	valid
12.0ms	98×	body	80	valid
9.0ms	36×	body	80	invalid
8.0ms	21×	body	320	valid
4.0ms	15×	body	160	valid
1.0ms	3×	body	320	invalid
1.0ms	1×	body	640	invalid
1.0ms	2×	body	160	invalid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5086	25

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 26.8b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
4.6b	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
6.5b	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
22.7b	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
106×	`prod-exp`
74×	`add-cbrt-cube`
40×	`cbrt-unprod`
37×	`associate-*r/`
30×	`div-exp`
22×	`associate-l`
14×	`add-sqr-sqrt`
12×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `pow-exp`
11×	`pow1`
10×	`associate-/r/`
9×	`tan-quot`
6×	`frac-times` `flip3-+` `times-frac` `flip-+`
5×	`associate-r` `associate-*l/`
4×	`pow-prod-down` `add-log-exp`
3×	`unpow-prod-down` `-commutative` `associate-/l`
2×	`div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*` `unswap-sqr` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

22.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
25.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
23.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
19.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
119.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
186.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
101.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5068	3715

prune288.0ms

Filtered

92 candidates to 164 candidates (-78.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	8	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	9	166

Merged error: 20.0b

Counts

166 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
4.6b	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
6.5b	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
17.1b	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

551×	`add-exp-log`
424×	`prod-exp`
85×	`add-cbrt-cube`
74×	`pow-exp`
66×	`div-exp`
52×	`cbrt-unprod`
50×	`pow-to-exp`
27×	`associate-*r/`
21×	`associate-l`
20×	`associate-*l/`
15×	`associate-r`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`cbrt-undiv`
9×	`tan-quot`
7×	`unpow-prod-down`
6×	`frac-times` `flip3-+` `flip-+`
5×	`associate-/r/`
4×	`pow-prod-down` `*-commutative` `add-log-exp`
3×	`cbrt-prod` `times-frac`
2×	`sqr-pow`
1×	`div-inv` `unswap-sqr`

Counts

4 → 210

Calls

4 calls:

18.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
31.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
33.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
24.0ms	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
133.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
206.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
117.0ms	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5033	6560

prune350.0ms

Filtered

90 candidates to 222 candidates (-146.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	216	6	222
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	218	13	231

Merged error: 17.2b

Counts

231 → 13

localize37.0ms

Local error

Found 4 expressions with local error:

4.6b	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
4.7b	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
5.2b	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
6.5b	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

1830×	`add-exp-log`
1542×	`prod-exp`
314×	`pow-exp`
183×	`pow-to-exp`
178×	`div-exp`
112×	`add-cbrt-cube`
73×	`cbrt-unprod`
32×	`associate-*l/`
27×	`associate-*r/`
21×	`associate-l`
12×	`cbrt-undiv` `add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`tan-quot`
6×	`frac-times` `flip3-+` `flip-+`
5×	`associate-/r/`
4×	`pow-prod-down` `*-commutative` `add-log-exp`
3×	`times-frac`
2×	`unpow-prod-down` `sqr-pow`
1×	`div-inv` `unswap-sqr`

Counts

4 → 391

Calls

4 calls:

41.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
24.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
30.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
37.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

series524.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
72.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
111.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
212.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

simplify135.0ms

Algorithm

egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5022	14013

prune386.0ms

Filtered

86 candidates to 403 candidates (-368.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	397	6	403
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	398	18	416

Merged error: 13.3b

Counts

416 → 18

localize38.0ms

Local error

Found 4 expressions with local error:

4.6b	(* l (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
5.4b	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
6.0b	(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
7.9b	(* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

4248×	`add-exp-log`
3108×	`prod-exp`
907×	`div-exp`
536×	`pow-exp`
308×	`pow-to-exp`
257×	`add-cbrt-cube`
200×	`cbrt-unprod`
63×	`cbrt-undiv`
34×	`associate-*r/`
20×	`pow1` `associate-l`
18×	`associate-r`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
11×	`times-frac`
10×	`pow-prod-down`
6×	`tan-quot` `frac-times`
5×	`associate-/r/`
4×	`flip3-+` `*-commutative` `flip-+` `add-log-exp`
3×	`cbrt-prod`
2×	`unpow-prod-down` `div-inv` `sqr-pow`
1×	`unswap-sqr`

Counts

4 → 679

Calls

4 calls:

51.0ms	(* l (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
24.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
39.0ms	(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
33.0ms	(* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* l (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
110.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
178.0ms	(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
149.0ms	(* l (/ (cbrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

simplify274.0ms

Algorithm

egg-herbie

Counts

691 → 691

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4969	29986
1	4969	29986

prune479.0ms

Filtered

90 candidates to 691 candidates (-667.8%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	681	10	691
Fresh	2	14	16
Picked	1	0	1
Done	0	1	1
Total	684	25	709

Merged error: 11.6b

Counts

709 → 25

regimes1.6s

Accuracy

16.2% (5.6b remaining)

Error of 18.3b against oracle of 12.8b and baseline of 19.4b

bsearch234.0ms

Steps

Iters	Range		Point
9	1.8458242798872947e+127	1.1965090957091683e+133	2.669625230460847e+132
10	-1.2758418589827206e-220	-6.3067005777648505e-232	-8.131248210282814e-222

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	165
1	86	165

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2075×	body	1280	valid
861.0ms	1523×	body	640	valid
456.0ms	3309×	body	80	valid
310.0ms	765×	body	320	valid
180.0ms	1408×	body	80	invalid
88.0ms	328×	body	160	valid
80.0ms	143×	body	640	invalid
46.0ms	100×	body	320	invalid
23.0ms	85×	body	160	invalid
18.0ms	23×	body	1280	invalid

Details

analyze2.2s

sample138.0ms

simplify23.0ms

prune16.0ms

localize25.0ms

rewrite98.0ms

series524.0ms

simplify48.0ms

prune288.0ms

localize28.0ms

rewrite124.0ms

series533.0ms

simplify82.0ms

prune350.0ms

localize37.0ms

rewrite188.0ms

series524.0ms

simplify135.0ms

prune386.0ms

localize38.0ms

rewrite274.0ms

series568.0ms

simplify274.0ms

prune479.0ms

regimes1.6s

bsearch234.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling