Details

sample477.0ms

Algorithm

intervals

Results

131.0ms	63×	body	2560	valid
127.0ms	26×	body	5120	valid
119.0ms	143×	body	1280	valid
53.0ms	89×	body	640	valid
11.0ms	29×	body	320	valid
7.0ms	53×	body	80	valid
3.0ms	12×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

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

prune14.0ms

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: 36.8b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
17.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite52.0ms

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))
17.0ms	(/ (* 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)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ k t) 2.0)
53.0ms	(* (pow t 3.0) (tan k))
111.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
66.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune319.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	180	13	193

Merged error: 24.2b

Counts

193 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
14.8b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
17.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
20.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite111.0ms

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

series295.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (pow t 3.0) (tan k))
66.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
111.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
65.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify81.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5002	5612

prune385.0ms

Filtered

109 candidates to 420 candidates (-285.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	416	4	420
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	421	12	433

Merged error: 24.2b

Counts

433 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (* l l) (sin k))
14.8b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
16.7b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
20.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite106.0ms

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:

5.0ms	(/ (* l l) (sin k))
19.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (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)))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
193.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
73.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify86.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune383.0ms

Filtered

106 candidates to 430 candidates (-305.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	422	8	430
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	426	16	442

Merged error: 20.9b

Counts

442 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (* l l) (sin k))
14.8b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
16.7b	(/ (* 2.0 (/ (* l l) (sin k))) (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
20.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

1903×	`add-exp-log`
1205×	`prod-exp`
585×	`div-exp`
422×	`pow-exp`
253×	`pow-to-exp`
103×	`add-cbrt-cube`
50×	`cbrt-unprod`
34×	`associate-l`
26×	`cbrt-undiv` `unpow-prod-down`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`associate-*r/`
4×	`pow1` `associate-/r*` `div-inv` `add-log-exp`
3×	`tan-quot`
2×	`frac-2neg` `associate-r` `clear-num` `-commutative` `associate-/l` `sqr-pow`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 471

Calls

4 calls:

5.0ms	(/ (* l l) (sin k))
18.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
25.0ms	(/ (* 2.0 (/ (* l l) (sin k))) (* (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)))

series252.0ms

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))))
108.0ms	(/ (* 2.0 (/ (* l l) (sin k))) (* (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)))

simplify92.0ms

Algorithm

egg-herbie

Counts

483 → 483

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1663	7606
1	5002	6304

prune244.0ms

Filtered

93 candidates to 483 candidates (-419.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	482	1	483
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	483	16	499

Merged error: 20.9b

Counts

499 → 16

regimes988.0ms

Accuracy

40.1% (7.2b remaining)

Error of 31.9b against oracle of 24.7b and baseline of 36.8b

bsearch461.0ms

Steps

Iters	Range	Point
10	5.2868730441662565e-111	1.48690115310721e-100	2.013940648706174e-108
7	-6.0290352596158254e-276	-1.0689403543015622e-277	-1.0816662756287496e-277
9	-1.4612837306014034e-101	-2.0507886861266856e-109	-1.980957473748411e-108

Iters

Range

Point

5.2868730441662565e-111

1.48690115310721e-100

2.013940648706174e-108

-6.0290352596158254e-276

-1.0689403543015622e-277

-1.0816662756287496e-277

-1.4612837306014034e-101

-2.0507886861266856e-109

-1.980957473748411e-108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	84
1	97	84

end0.0ms

sample15.3s

Algorithm

intervals

Results

4.6s	2255×	body	2560	valid
4.6s	983×	body	5120	valid
3.3s	4090×	body	1280	valid
1.4s	2545×	body	640	valid
386.0ms	996×	body	320	valid
269.0ms	2103×	body	80	valid
118.0ms	466×	body	160	valid

Details

sample477.0ms

simplify27.0ms

prune14.0ms

localize19.0ms

rewrite52.0ms

series243.0ms

simplify45.0ms

prune319.0ms

localize21.0ms

rewrite111.0ms

series295.0ms

simplify81.0ms

prune385.0ms

localize21.0ms

rewrite106.0ms

series344.0ms

simplify86.0ms

prune383.0ms

localize21.0ms

rewrite117.0ms

series252.0ms

simplify92.0ms

prune244.0ms

regimes988.0ms

bsearch461.0ms

simplify2.0ms

end0.0ms

sample15.3s

Profiling