Details

sample10.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 2.618408%

Guaranteed chance to sample good point: 4.638045%

Results

109.0ms	28×	body	5120	invalid
96.0ms	110×	body	1280	valid
80.0ms	36×	body	2560	invalid
47.0ms	31×	body	2560	valid
33.0ms	61×	body	640	valid
23.0ms	23×	body	1280	invalid
16.0ms	6×	body	5120	valid
8.0ms	17×	body	640	invalid
8.0ms	21×	body	320	valid
6.0ms	39×	body	80	invalid
3.0ms	8×	body	320	invalid
3.0ms	20×	body	80	valid
2.0ms	8×	body	160	invalid
2.0ms	7×	body	160	valid

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

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: 37.7b

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))
21.4b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
25.2b	(* (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:

13.0ms	(pow (/ k t) 2.0)
51.0ms	(* (pow t 3.0) (tan k))
113.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
67.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune301.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	178	13	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	179	14	193

Merged error: 27.3b

Counts

193 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
13.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
16.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
21.4b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

rewrite103.0ms

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

series296.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (pow t 3.0) (tan k))
65.0ms	(* (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)))
112.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

simplify86.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5001	5612

prune400.0ms

Filtered

111 candidates to 420 candidates (-278.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	413	7	420
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	420	14	434

Merged error: 27.3b

Counts

434 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* l l) (sin k))
13.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
16.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
20.1b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

rewrite100.0ms

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))
15.0ms	(* (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)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* l l) (sin k))
65.0ms	(* (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)))
198.0ms	(* (/ 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 (26.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune361.0ms

Filtered

107 candidates to 430 candidates (-301.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	420	10	430
Fresh	7	6	13
Picked	0	1	1
Done	0	0	0
Total	427	17	444

Merged error: 23.2b

Counts

444 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
13.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
16.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
20.1b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (* l (/ l (sin k))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1101×	`prod-exp`
413×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
53×	`cbrt-unprod`
49×	`associate-l`
30×	`add-sqr-sqrt` `unpow-prod-down`
25×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
17×	`cbrt-undiv`
12×	`associate-*r/`
9×	`pow1`
6×	`associate-r`
4×	`tan-quot` `*-commutative` `add-log-exp` `sqr-pow`
3×	`pow-prod-down` `div-inv` `unswap-sqr`
1×	`frac-times` `associate-*l/` `associate-/r/`

Counts

4 → 416

Calls

4 calls:

5.0ms	(* (pow t 3.0) (tan k))
15.0ms	(* (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)))
27.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (* l (/ l (sin k))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (pow t 3.0) (tan 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)))
198.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (* l (/ l (sin k))))

simplify85.0ms

Algorithm

egg-herbie

Counts

428 → 428

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1724	6568
1	5002	5372

prune276.0ms

Filtered

103 candidates to 428 candidates (-315.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	424	4	428
Fresh	3	12	15
Picked	1	0	1
Done	0	1	1
Total	428	17	445

Merged error: 22.2b

Counts

445 → 17

regimes826.0ms

Accuracy

40.7% (7.3b remaining)

Error of 30.6b against oracle of 23.3b and baseline of 35.7b

bsearch496.0ms

Steps

Iters	Range	Point
10	5.37250911704879e-143	5.949319910235258e-124	5.832499001294496e-124
10	-1.9873738521681822e-294	3.71335197084921e-308	-5.93371263119561e-309
10	-1.4074945333252848e-96	-5.311917754548566e-110	-1.804694207801877e-108

Iters

Range

Point

5.37250911704879e-143

5.949319910235258e-124

5.832499001294496e-124

-1.9873738521681822e-294

3.71335197084921e-308

-5.93371263119561e-309

-1.4074945333252848e-96

-5.311917754548566e-110

-1.804694207801877e-108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	86
1	97	86

end0.0ms

sample24.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 2.618408%

Guaranteed chance to sample good point: 4.638045%

Results

3.4s	715×	body	5120	invalid
3.3s	1233×	body	2560	invalid
2.8s	3285×	body	1280	valid
1.4s	966×	body	2560	valid
1.1s	1914×	body	640	valid
675.0ms	219×	body	5120	valid
649.0ms	759×	body	1280	invalid
282.0ms	547×	body	640	invalid
278.0ms	663×	body	320	valid
148.0ms	1068×	body	80	invalid
141.0ms	353×	body	320	invalid
96.0ms	695×	body	80	valid
70.0ms	258×	body	160	valid
49.0ms	188×	body	160	invalid

Details

sample10.4s

simplify27.0ms

prune13.0ms

localize19.0ms

rewrite51.0ms

series244.0ms

simplify45.0ms

prune301.0ms

localize21.0ms

rewrite103.0ms

series296.0ms

simplify86.0ms

prune400.0ms

localize23.0ms

rewrite100.0ms

series341.0ms

simplify80.0ms

prune361.0ms

localize21.0ms

rewrite99.0ms

series384.0ms

simplify85.0ms

prune276.0ms

regimes826.0ms

bsearch496.0ms

simplify2.0ms

end0.0ms

sample24.9s

Profiling