Details

sample22.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.937744%

Guaranteed chance to sample good point: 1.617978%

Results

107.0ms	30×	body	5120	invalid
86.0ms	109×	body	1280	valid
85.0ms	40×	body	2560	invalid
44.0ms	31×	body	2560	valid
25.0ms	46×	body	640	valid
19.0ms	6×	body	5120	valid
17.0ms	22×	body	1280	invalid
12.0ms	23×	body	640	invalid
10.0ms	25×	body	320	valid
4.0ms	12×	body	320	invalid
4.0ms	26×	body	80	valid
3.0ms	13×	body	160	valid
3.0ms	21×	body	80	invalid
1.0ms	3×	body	160	invalid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

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: 37.3b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.3b	(* (pow t 3.0) (tan k))
20.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.9b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite67.0ms

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))
19.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ k t) 2.0)
52.0ms	(* (pow t 3.0) (tan k))
106.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
68.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify47.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune324.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	176	15	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	16	193

Merged error: 27.1b

Counts

193 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (pow t 3.0) (tan k))
16.0b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
17.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
20.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

rewrite105.0ms

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:

5.0ms	(* (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)))
28.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

series300.0ms

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))))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
114.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

simplify87.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5001	5612

prune402.0ms

Filtered

108 candidates to 420 candidates (-288.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	416	4	420
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	421	15	436

Merged error: 27.1b

Counts

436 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (* l l) (sin k))
16.0b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
17.4b	(* (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:

7.0ms	(/ (* l l) (sin k))
16.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
10.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
28.0ms	(* (/ 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))
67.0ms	(* (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

prune384.0ms

Filtered

106 candidates to 430 candidates (-305.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	421	9	430
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	425	20	445

Merged error: 21.0b

Counts

445 → 20

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (* l l) (sin k))
15.4b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
15.4b	(* (/ 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))))
17.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite213.0ms

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))
17.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
41.0ms	(* (/ 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)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
192.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
194.0ms	(* (/ 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))))
74.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify198.0ms

Algorithm

egg-herbie

Counts

987 → 987

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	3075	17702
1	5002	16681

prune522.0ms

Filtered

156 candidates to 987 candidates (-532.7%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	981	6	987
Fresh	2	16	18
Picked	1	0	1
Done	1	0	1
Total	985	22	1007

Merged error: 19.5b

Counts

1007 → 22

regimes840.0ms

Accuracy

45.9% (5.4b remaining)

Error of 27.6b against oracle of 22.2b and baseline of 32.2b

bsearch563.0ms

Steps

Iters	Range	Point
10	1.4386591911410254e-93	5.780800601426271e-79	1.4613983394965043e-93
7	-5.316992075641663e-288	-4.8237984564084705e-290	-4.891327558394279e-290
7	-8.289053229613869e-85	-1.0091187824356869e-86	-1.0290870676888813e-86

Iters

Range

Point

1.4386591911410254e-93

5.780800601426271e-79

1.4613983394965043e-93

-5.316992075641663e-288

-4.8237984564084705e-290

-4.891327558394279e-290

-8.289053229613869e-85

-1.0091187824356869e-86

-1.0290870676888813e-86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	84
1	94	84

end0.0ms

sample37.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.937744%

Guaranteed chance to sample good point: 1.617978%

Results

3.6s	763×	body	5120	invalid
3.2s	1259×	body	2560	invalid
2.8s	3279×	body	1280	valid
1.4s	921×	body	2560	valid
1.1s	1983×	body	640	valid
715.0ms	220×	body	5120	valid
657.0ms	778×	body	1280	invalid
292.0ms	565×	body	640	invalid
265.0ms	652×	body	320	valid
132.0ms	345×	body	320	invalid
104.0ms	742×	body	80	invalid
92.0ms	670×	body	80	valid
78.0ms	275×	body	160	valid
49.0ms	198×	body	160	invalid

Details

sample22.8s

simplify27.0ms

prune14.0ms

localize18.0ms

rewrite67.0ms

series239.0ms

simplify47.0ms

prune324.0ms

localize20.0ms

rewrite105.0ms

series300.0ms

simplify87.0ms

prune402.0ms

localize21.0ms

rewrite102.0ms

series343.0ms

simplify80.0ms

prune384.0ms

localize22.0ms

rewrite213.0ms

series470.0ms

simplify198.0ms

prune522.0ms

regimes840.0ms

bsearch563.0ms

simplify2.0ms

end0.0ms

sample37.7s

Profiling