Details

analyze2.8s

Algorithm: search

sample599.0ms

Algorithm

intervals

Results

189.0ms	25×	body	5120	invalid
128.0ms	47×	body	2560	invalid
105.0ms	114×	body	1280	valid
45.0ms	73×	body	640	valid
35.0ms	26×	body	2560	valid
28.0ms	34×	body	1280	invalid
28.0ms	10×	body	5120	valid
6.0ms	15×	body	320	valid
5.0ms	12×	body	640	invalid
4.0ms	32×	body	80	invalid
4.0ms	11×	body	320	invalid
3.0ms	14×	body	80	valid
1.0ms	4×	body	160	valid
1.0ms	3×	body	160	invalid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune13.0ms

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: 38.8b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
21.3b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
5.0ms	(* (pow t 3.0) (tan k))
20.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ k t) 2.0)
51.0ms	(* (pow t 3.0) (tan k))
108.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
72.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify46.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune289.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	183	10	193

Merged error: 29.9b

Counts

193 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
12.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
18.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
21.3b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1168×	`prod-exp`
346×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
55×	`cbrt-unprod`
41×	`associate-l`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`cbrt-undiv`
9×	`associate-*r/`
5×	`associate-r`
4×	`tan-quot` `pow1` `add-log-exp` `sqr-pow`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 408

Calls

4 calls:

6.0ms	(* (pow t 3.0) (tan k))
19.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
30.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (pow t 3.0) (tan k))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
66.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
118.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

simplify81.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5001	5612

prune369.0ms

Filtered

109 candidates to 420 candidates (-285.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	416	4	420
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	417	13	430

Merged error: 29.4b

Counts

430 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (* l l) (sin k))
12.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
18.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
19.5b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1029×	`prod-exp`
485×	`div-exp`
340×	`pow-exp`
204×	`pow-to-exp`
98×	`add-cbrt-cube`
48×	`cbrt-unprod`
42×	`associate-l`
30×	`add-sqr-sqrt`
28×	`times-frac`
26×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
24×	`cbrt-undiv`
9×	`associate-r/` `associate-r*`
6×	`pow1`
5×	`div-inv`
4×	`add-log-exp`
3×	`tan-quot` `associate-/r` `-commutative`
2×	`unswap-sqr` `sqr-pow`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `associate-/l`

Counts

4 → 418

Calls

4 calls:

4.0ms	(/ (* l l) (sin k))
16.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
29.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
197.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

simplify80.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune353.0ms

Filtered

106 candidates to 430 candidates (-305.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	423	7	430
Fresh	3	8	11
Picked	1	0	1
Done	1	0	1
Total	428	15	443

Merged error: 24.3b

Counts

443 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (* l l) (sin k))
12.3b	(* (/ 1 (pow (/ k t) (/ 2.0 2))) (* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
18.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
18.6b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

4987×	`add-exp-log`
2928×	`prod-exp`
1997×	`div-exp`
846×	`pow-exp`
509×	`pow-to-exp`
220×	`rec-exp` `1-exp`
217×	`add-cbrt-cube`
105×	`cbrt-unprod`
97×	`times-frac`
80×	`associate-l`
66×	`cbrt-undiv`
64×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
11×	`pow1`
10×	`associate-*r/`
9×	`associate-r`
8×	`div-inv`
6×	`frac-times`
4×	`pow-prod-down` `associate-*l/` `add-log-exp` `sqr-pow`
3×	`associate-/r` `-commutative`
2×	`tan-quot` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 975

Calls

4 calls:

5.0ms	(/ (* l l) (sin k))
45.0ms	(* (/ 1 (pow (/ k t) (/ 2.0 2))) (* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
18.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
193.0ms	(* (/ 1 (pow (/ k t) (/ 2.0 2))) (* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
196.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))

simplify191.0ms

Algorithm

egg-herbie

Counts

987 → 987

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	3075	17702
1	5002	16681

prune488.0ms

Filtered

156 candidates to 987 candidates (-532.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	981	6	987
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	983	19	1002

Merged error: 22.4b

Counts

1002 → 19

regimes991.0ms

Accuracy

28.5% (7.4b remaining)

Error of 29.9b against oracle of 22.6b and baseline of 32.9b

bsearch2.4s

Steps

Iters	Range		Point
9	5.292773144639518e-143	1.4777632415075824e-133	1.4507735559258041e-133
7	-2.3838405837039875e-56	-1.266078505786151e-58	-1.289662399796905e-58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	33
1	54	33
2	54	33

end0.0ms

analyze2.6s

Algorithm: search

sample14.6s

Algorithm

intervals

Results

3.5s	693×	body	5120	invalid
3.1s	1225×	body	2560	invalid
2.8s	3327×	body	1280	valid
1.4s	935×	body	2560	valid
1.2s	2007×	body	640	valid
666.0ms	767×	body	1280	invalid
622.0ms	199×	body	5120	valid
268.0ms	529×	body	640	invalid
263.0ms	640×	body	320	valid
129.0ms	345×	body	320	invalid
123.0ms	919×	body	80	invalid
105.0ms	646×	body	80	valid
65.0ms	246×	body	160	valid
53.0ms	209×	body	160	invalid

Details

analyze2.8s

sample599.0ms

simplify26.0ms

prune13.0ms

localize19.0ms

rewrite51.0ms

series244.0ms

simplify46.0ms

prune289.0ms

localize22.0ms

rewrite106.0ms

series302.0ms

simplify81.0ms

prune369.0ms

localize23.0ms

rewrite102.0ms

series343.0ms

simplify80.0ms

prune353.0ms

localize25.0ms

rewrite208.0ms

series468.0ms

simplify191.0ms

prune488.0ms

regimes991.0ms

bsearch2.4s

simplify2.0ms

end0.0ms

analyze2.6s

sample14.6s

Profiling