Details

analyze9.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 5.076928%

Guaranteed chance to sample good point: 1.617978%

sample544.0ms

Algorithm

intervals

Results

140.0ms	44×	body	2560	invalid
136.0ms	35×	body	5120	invalid
86.0ms	103×	body	1280	valid
36.0ms	63×	body	640	valid
32.0ms	12×	body	5120	valid
30.0ms	22×	body	2560	valid
23.0ms	28×	body	1280	invalid
13.0ms	21×	body	320	valid
7.0ms	13×	body	640	invalid
5.0ms	12×	body	320	invalid
5.0ms	31×	body	80	invalid
4.0ms	27×	body	80	valid
4.0ms	14×	body	160	invalid
2.0ms	8×	body	160	valid

simplify28.0ms

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: 39.9b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
19.3b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
31.5b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite46.0ms

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))
16.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
10.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series240.0ms

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)))

simplify45.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune313.0ms

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: 29.3b

Counts

193 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
16.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.3b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
22.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite98.0ms

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))))
27.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
10.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (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))))
106.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
71.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify86.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5002	5612

prune411.0ms

Filtered

109 candidates to 420 candidates (-285.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	416	4	420
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	418	15	433

Merged error: 29.2b

Counts

433 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b	(/ (* l l) (sin k))
16.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
17.0b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
22.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite99.0ms

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))))
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)))
10.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (* l l) (sin k))
66.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
191.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
70.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify79.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune390.0ms

Filtered

106 candidates to 430 candidates (-305.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	422	8	430
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	426	19	445

Merged error: 23.2b

Counts

445 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b	(/ (* l l) (sin k))
14.0b	(* (/ 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))))
16.5b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
22.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite211.0ms

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:

4.0ms	(/ (* l l) (sin k))
40.0ms	(* (/ 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))))
17.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
10.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (* l l) (sin k))
190.0ms	(* (/ 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))))
192.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
64.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify199.0ms

Algorithm

egg-herbie

Counts

987 → 987

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	3075	17702
1	5002	16681

prune509.0ms

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	5	13	18
Picked	1	0	1
Done	0	0	0
Total	987	19	1006

Merged error: 22.2b

Counts

1006 → 19

Details

analyze9.1s

sample544.0ms

simplify28.0ms

prune14.0ms

localize22.0ms

rewrite46.0ms

series240.0ms

simplify45.0ms

prune313.0ms

localize21.0ms

rewrite98.0ms

series294.0ms

simplify86.0ms

prune411.0ms

localize22.0ms

rewrite99.0ms

series337.0ms

simplify79.0ms

prune390.0ms

localize22.0ms

rewrite211.0ms

series456.0ms

simplify199.0ms

prune509.0ms

regimes1.1s

bsearch1.0ms

Profiling