Details

sample112.0ms

Algorithm

intervals

Results

42.0ms	63×	body	1280	valid
24.0ms	52×	body	640	valid
20.0ms	195×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	13
1	158	13
2	903	13
3	5001	13

prune4.0ms

Filtered

1 candidates to 0 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: 31.8b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.9b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.6b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.9b	(/ (pow t 3.0) (* l l))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

865×	`associate-l`
747×	`add-sqr-sqrt`
510×	`times-frac`
376×	`associate-*l/`
351×	`*-un-lft-identity`
346×	`add-cube-cbrt`
240×	`unpow-prod-down`
221×	`unswap-sqr`
202×	`frac-times`
150×	`associate-/r*`
134×	`associate-r`
132×	`swap-sqr`
108×	`add-exp-log`
104×	`tan-quot`
100×	`sqr-pow`
70×	`associate-/l*`
62×	`*-commutative`
58×	`prod-exp`
52×	`flip3-+` `add-cbrt-cube` `flip-+`
26×	`cbrt-unprod`
24×	`div-exp`
20×	`pow1`
10×	`frac-2neg` `pow-prod-down` `clear-num`
8×	`cbrt-undiv` `pow-to-exp` `pow-exp`
6×	`associate-*r/`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `div-inv` `add-log-exp`
3×	`distribute-lft-out`

Counts

4 → 912

Calls

4 calls:

50.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
35.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
96.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
12.0ms	(/ (pow t 3.0) (* l l))

series1.5s

Counts

4 → 12

Calls

4 calls:

338.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
258.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
670.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
197.0ms	(/ (pow t 3.0) (* l l))

simplify189.0ms

Algorithm

egg-herbie

Counts

924 → 924

Iterations

Useful iterations: 1 (70.0ms)

Iter	Nodes	Cost
0	3751	10837
1	5001	10742

prune3.0s

Filtered

924 candidates to 616 candidates (66.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	908	16	924
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	909	16	925

Merged error: 14.2b

Counts

925 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l))
5.6b	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l)))
8.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.2b	(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

14718×	`frac-times`
11132×	`associate-/l*`
7596×	`add-sqr-sqrt`
7196×	`unpow-prod-down`
5826×	`associate-*r/`
4085×	`cbrt-prod`
3935×	`*-un-lft-identity`
3824×	`associate-l`
3689×	`add-cube-cbrt`
3422×	`tan-quot`
2379×	`flip3-+` `flip-+`
2354×	`associate-r`
2136×	`unswap-sqr`
1260×	`associate-/r*`
1156×	`swap-sqr`
705×	`sqr-pow`
557×	`times-frac`
538×	`clear-num`
449×	`*-commutative`
420×	`frac-2neg`
354×	`un-div-inv`
234×	`add-exp-log`
233×	`associate-*l/`
135×	`prod-exp`
74×	`add-cbrt-cube`
60×	`div-exp`
38×	`cbrt-unprod`
23×	`pow-exp`
20×	`pow1`
15×	`pow-to-exp`
14×	`cbrt-undiv`
10×	`pow-prod-down`
6×	`distribute-lft-out`
5×	`div-inv`
4×	`add-log-exp`

Counts

4 → 7899

Calls

4 calls:

36.0ms	(* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l))
70.0ms	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l)))
15.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
372.0ms	(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l))))

series1.7s

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l))
422.0ms	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l)))
196.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
728.0ms	(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (tan k) (/ (* (pow (cbrt t) 3.0) (sin k)) l))))

simplify2.9s

Algorithm

egg-herbie

Counts

7911 → 7911

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	9389	272895

prune41.0s

Filtered

7911 candidates to 6112 candidates (77.3%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	7888	23	7911
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	7898	29	7927

Merged error: 7.3b

Counts

7927 → 29

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
0.8b	(/ l (* (pow (cbrt t) 3.0) (sin k)))
3.3b	(* (pow (sqrt (* (cbrt t) (cbrt t))) 3.0) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
10.1b	(/ (* (pow (sqrt (* (cbrt t) (cbrt t))) 3.0) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1))) (* (/ l (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) (* (cos k) (/ l (* (pow (cbrt t) 3.0) (sin k))))))

rewrite9.6s

Algorithm

rewrite-expression-head

Rules

129540×	`add-sqr-sqrt`
71446×	`unswap-sqr`
69092×	`times-frac`
45624×	`unpow-prod-down`
35397×	`sqrt-prod`
34779×	`associate-r`
32358×	`associate-l`
25423×	`cbrt-prod`
23502×	`*-un-lft-identity`
17989×	`add-cube-cbrt`
7866×	`swap-sqr`
4982×	`sqr-pow`
4090×	`*-commutative`
2264×	`associate-/r*`
2237×	`add-exp-log`
1433×	`prod-exp`
1270×	`associate-/r/`
1200×	`frac-times`
1182×	`associate-*r/`
864×	`distribute-lft-out`
771×	`div-exp`
373×	`associate-/l*`
240×	`add-cbrt-cube`
236×	`pow-to-exp` `pow-exp`
230×	`div-inv`
125×	`cbrt-unprod`
115×	`clear-num`
82×	`un-div-inv`
78×	`1-exp`
74×	`frac-2neg`
70×	`cbrt-undiv`
44×	`associate-*l/`
14×	`pow1`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `flip3-+` `flip-+` `associate-/l/`
1×	`pow1/3`

Counts

4 → 34624

Calls

4 calls:

2.0ms	(pow (cbrt t) 3.0)
12.0ms	(/ l (* (pow (cbrt t) 3.0) (sin k)))
54.0ms	(* (pow (sqrt (* (cbrt t) (cbrt t))) 3.0) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
1.1s	(/ (* (pow (sqrt (* (cbrt t) (cbrt t))) 3.0) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1))) (* (/ l (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) (* (cos k) (/ l (* (pow (cbrt t) 3.0) (sin k))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

327.0ms	(pow (cbrt t) 3.0)
299.0ms	(/ l (* (pow (cbrt t) 3.0) (sin k)))
418.0ms	(* (pow (sqrt (* (cbrt t) (cbrt t))) 3.0) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
544.0ms	(/ (* (pow (sqrt (* (cbrt t) (cbrt t))) 3.0) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1))) (* (/ l (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) (* (cos k) (/ l (* (pow (cbrt t) 3.0) (sin k))))))

simplify16.0s

Algorithm

egg-herbie

Counts

34636 → 34636

Iterations

Useful iterations: 0 (741.0ms)

Iter	Nodes	Cost
0	34730	1806636

prune3.3m

Filtered

34636 candidates to 21733 candidates (62.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	34622	14	34636
Fresh	17	11	28
Picked	1	0	1
Done	0	0	0
Total	34640	25	34665

Merged error: 7.0b

Counts

34665 → 25

localize55.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1))) (* (/ (cbrt l) (pow (sqrt (* (cbrt (cbrt t)) (cbrt (cbrt t)))) 3.0)) (* (cos k) (/ l (* (pow (cbrt t) 3.0) (sin k))))))
16.7b	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
16.7b	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
16.7b	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))

rewrite5.4s

Algorithm

rewrite-expression-head

Rules

65874×	`add-sqr-sqrt`
48143×	`cbrt-prod`
42440×	`times-frac`
29949×	`unswap-sqr`
19468×	`unpow-prod-down`
17381×	`associate-l`
17267×	`associate-r`
16146×	`*-un-lft-identity`
14951×	`sqrt-prod`
11580×	`add-cube-cbrt`
3404×	`associate-/r*`
3159×	`swap-sqr`
2127×	`*-commutative`
2067×	`sqr-pow`
1932×	`distribute-lft-out`
1797×	`associate-/r/`
1710×	`frac-times`
1654×	`associate-*r/`
447×	`associate-/l*`
148×	`clear-num`
134×	`add-exp-log`
116×	`un-div-inv`
111×	`add-cbrt-cube`
90×	`frac-2neg`
65×	`associate-*l/`
61×	`div-inv`
59×	`div-exp`
56×	`prod-exp`
54×	`cbrt-undiv`
48×	`cbrt-unprod`
10×	`pow-to-exp` `pow-exp`
8×	`cbrt-div`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3`
2×	`associate-/l/`

Counts

4 → 21197

Calls

4 calls:

939.0ms	(/ (cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1))) (* (/ (cbrt l) (pow (sqrt (* (cbrt (cbrt t)) (cbrt (cbrt t)))) 3.0)) (* (cos k) (/ l (* (pow (cbrt t) 3.0) (sin k))))))
19.0ms	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
18.0ms	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
21.0ms	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))

series1.2s

Counts

4 → 12

Calls

4 calls:

607.0ms	(/ (cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1))) (* (/ (cbrt l) (pow (sqrt (* (cbrt (cbrt t)) (cbrt (cbrt t)))) 3.0)) (* (cos k) (/ l (* (pow (cbrt t) 3.0) (sin k))))))
188.0ms	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
188.0ms	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))
198.0ms	(cbrt (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (* (sin k) 1)))

simplify8.9s

Algorithm

egg-herbie

Counts

21209 → 21209

Iterations

Useful iterations: 0 (325.0ms)

Iter	Nodes	Cost
0	22355	1006240

prune3.6m

Filtered

21209 candidates to 15130 candidates (71.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	21204	5	21209
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	21209	25	21234

Merged error: 7.0b

Counts

21234 → 25

regimes739.0ms

Accuracy

0% (5.0b remaining)

Error of 12.1b against oracle of 7.1b and baseline of 12.1b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	103
1	65	103
2	65	103

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	2034×	body	1280	valid
900.0ms	1737×	body	640	valid
656.0ms	5832×	body	80	valid
320.0ms	859×	body	320	valid
121.0ms	451×	body	160	valid

Details

sample112.0ms

simplify32.0ms

prune4.0ms

localize27.0ms

rewrite277.0ms

series1.5s

simplify189.0ms

prune3.0s

localize27.0ms

rewrite1.7s

series1.7s

simplify2.9s

prune41.0s

localize33.0ms

rewrite9.6s

series1.6s

simplify16.0s

prune3.3m

localize55.0ms

rewrite5.4s

series1.2s

simplify8.9s

prune3.6m

regimes739.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample3.9s

end1.5m