Details

sample564.0ms

Algorithm

intervals

Results

191.0ms	39×	body	5120	valid
153.0ms	70×	body	2560	valid
93.0ms	118×	body	1280	valid
46.0ms	85×	body	640	valid
10.0ms	76×	body	80	valid
10.0ms	26×	body	320	valid
3.0ms	14×	body	160	valid

simplify26.0ms

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: 39.2b

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))
21.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.7b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite47.0ms

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

series242.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ k t) 2.0)
52.0ms	(* (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)))
69.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify43.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune280.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	9	193

Merged error: 27.7b

Counts

193 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
14.3b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
15.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
21.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

rewrite107.0ms

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)))
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)))

series295.0ms

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)))
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)))

simplify85.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5001	5612

prune397.0ms

Filtered

111 candidates to 420 candidates (-278.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	415	5	420
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	417	12	429

Merged error: 27.4b

Counts

429 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* l l) (sin k))
14.3b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
15.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
19.4b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

rewrite113.0ms

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))
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)))
32.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

series336.0ms

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))))
66.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
195.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

simplify83.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune376.0ms

Filtered

107 candidates to 430 candidates (-301.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	424	6	430
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	427	15	442

Merged error: 24.9b

Counts

442 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* l l) (sin k))
13.8b	(* (/ 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))))
15.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
17.1b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))

rewrite218.0ms

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))
39.0ms	(* (/ 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))))
12.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
17.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))

series464.0ms

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))))
65.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
195.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))

simplify189.0ms

Algorithm

egg-herbie

Counts

987 → 987

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	3075	17702
1	5002	16681

prune468.0ms

Filtered

157 candidates to 987 candidates (-528.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	980	7	987
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	986	16	1002

Merged error: 22.6b

Counts

1002 → 16

regimes698.0ms

Accuracy

47.4% (5.3b remaining)

Error of 28.1b against oracle of 22.8b and baseline of 32.9b

bsearch470.0ms

Steps

Iters	Range	Point
8	3.7990141414424663e-118	2.3399544250992457e-113	2.2996398703167197e-113
10	-9.83283237816018e-279	-1.3490407598345e-289	-1.3671182285278927e-289
9	-7.158279884007304e-109	-2.630809891269091e-118	-7.027903503439177e-109

Iters

Range

Point

3.7990141414424663e-118

2.3399544250992457e-113

2.2996398703167197e-113

-9.83283237816018e-279

-1.3490407598345e-289

-1.3671182285278927e-289

-7.158279884007304e-109

-2.630809891269091e-118

-7.027903503439177e-109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	91
1	105	91

end0.0ms

sample14.2s

Algorithm

intervals

Results

4.1s	2117×	body	2560	valid
4.0s	929×	body	5120	valid
3.4s	4112×	body	1280	valid
1.4s	2509×	body	640	valid
375.0ms	963×	body	320	valid
282.0ms	2083×	body	80	valid
120.0ms	463×	body	160	valid

Details

sample564.0ms

simplify26.0ms

prune14.0ms

localize22.0ms

rewrite47.0ms

series242.0ms

simplify43.0ms

prune280.0ms

localize20.0ms

rewrite107.0ms

series295.0ms

simplify85.0ms

prune397.0ms

localize21.0ms

rewrite113.0ms

series336.0ms

simplify83.0ms

prune376.0ms

localize22.0ms

rewrite218.0ms

series464.0ms

simplify189.0ms

prune468.0ms

regimes698.0ms

bsearch470.0ms

simplify2.0ms

end0.0ms

sample14.2s

Profiling