Details

sample498.0ms

Algorithm

intervals

Results

231.0ms	32×	body	5120	valid
100.0ms	50×	body	2560	valid
84.0ms	123×	body	1280	valid
42.0ms	88×	body	640	valid
11.0ms	36×	body	320	valid
7.0ms	62×	body	80	valid
4.0ms	18×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

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

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 37.4b

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))
18.2b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.3b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

5057×	`add-sqr-sqrt`
2843×	`associate-l`
2812×	`unswap-sqr`
2783×	`times-frac`
2196×	`associate-r`
1235×	`unpow-prod-down`
1036×	`add-cube-cbrt` `*-un-lft-identity`
565×	`sqr-pow`
337×	`add-exp-log`
336×	`*-commutative`
328×	`swap-sqr`
220×	`prod-exp`
81×	`associate-/r*`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
32×	`div-inv`
28×	`associate-/l*`
12×	`pow1` `cbrt-undiv`
5×	`associate-*r/`
4×	`pow-prod-down` `add-log-exp`
3×	`tan-quot` `pow-unpow`
1×	`pow-pow` `frac-2neg` `associate-*l/` `clear-num` `associate-/r/`

Counts

4 → 2589

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
96.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
19.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ k t) 2.0)
250.0ms	(* (pow t 3.0) (tan k))
376.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
255.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify545.0ms

Algorithm

egg-herbie

Counts

2601 → 2601

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5001	53883

prune8.4s

Filtered

2601 candidates to 1663 candidates (63.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	2580	21	2601
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	2582	21	2603

Merged error: 9.8b

Counts

2603 → 21

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.3b	(* (pow k 2.0) (pow t 1.0))
14.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

2158×	`add-sqr-sqrt`
1645×	`add-exp-log`
1373×	`unswap-sqr`
1368×	`times-frac`
1282×	`unpow-prod-down`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
623×	`sqr-pow`
509×	`pow-to-exp`
471×	`*-un-lft-identity`
364×	`associate-r`
285×	`unpow2`
259×	`add-cube-cbrt`
203×	`associate-l`
140×	`rec-exp` `1-exp`
45×	`associate-/l*`
44×	`associate-/r*`
31×	`associate-*r/`
27×	`*-commutative`
25×	`add-cbrt-cube`
11×	`pow1`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
4×	`clear-num` `div-inv` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `un-div-inv`
2×	`pow-flip`
1×	`inv-pow`

Counts

4 → 1628

Calls

4 calls:

15.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
15.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.0ms	(* (pow k 2.0) (pow t 1.0))
220.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

351.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
93.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
346.0ms	(* (pow k 2.0) (pow t 1.0))
668.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify346.0ms

Algorithm

egg-herbie

Counts

1640 → 1640

Iterations

Useful iterations: 1 (85.0ms)

Iter	Nodes	Cost
0	4705	28157
1	5001	26518

prune2.9s

Filtered

1640 candidates to 553 candidates (33.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	1630	10	1640
Fresh	9	11	20
Picked	1	0	1
Done	0	0	0
Total	1640	21	1661

Merged error: 4.0b

Counts

1661 → 21

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (pow l (/ 2 2)) (pow (sin k) 2))
2.1b	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
6.3b	(* (pow k 2.0) (pow t 1.0))
7.8b	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

rewrite813.0ms

Algorithm

rewrite-expression-head

Rules

3155×	`add-sqr-sqrt`
3120×	`add-exp-log`
2362×	`prod-exp`
2251×	`unswap-sqr`
1681×	`unpow-prod-down`
1492×	`pow-exp`
1444×	`times-frac`
1052×	`div-exp`
832×	`pow-to-exp`
811×	`sqr-pow`
475×	`*-un-lft-identity`
299×	`associate-r`
234×	`associate-l`
220×	`rec-exp` `1-exp`
174×	`add-cube-cbrt`
157×	`unpow2`
34×	`add-cbrt-cube`
20×	`pow1`
18×	`associate-*r/`
16×	`associate-/r*` `cbrt-unprod`
15×	`associate-/l*`
12×	`*-commutative`
10×	`pow-prod-down`
4×	`cbrt-undiv` `div-inv` `add-log-exp`
3×	`clear-num`
2×	`frac-2neg` `un-div-inv`

Counts

4 → 1894

Calls

4 calls:

10.0ms	(/ (pow l (/ 2 2)) (pow (sin k) 2))
204.0ms	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
10.0ms	(* (pow k 2.0) (pow t 1.0))
59.0ms	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (pow l (/ 2 2)) (pow (sin k) 2))
415.0ms	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
344.0ms	(* (pow k 2.0) (pow t 1.0))
282.0ms	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

simplify407.0ms

Algorithm

egg-herbie

Counts

1906 → 1906

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5001	39193

prune3.7s

Filtered

1906 candidates to 655 candidates (34.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1894	12	1906
Fresh	12	8	20
Picked	1	0	1
Done	0	0	0
Total	1907	20	1927

Merged error: 1.3b

Counts

1927 → 20

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1b	(* (* (* (cos k) l) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2))))
1.4b	(/ (pow l 1) (pow (sin k) 2))
3.9b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

44033×	`add-exp-log`
35818×	`prod-exp`
31872×	`add-sqr-sqrt`
26518×	`pow-exp`
25111×	`unswap-sqr`
18291×	`unpow-prod-down`
16923×	`div-exp`
15309×	`times-frac`
12760×	`pow-to-exp`
8873×	`sqr-pow`
4805×	`*-un-lft-identity`
4596×	`rec-exp` `1-exp`
1473×	`unpow2`
678×	`associate-r`
333×	`associate-l`
267×	`add-cube-cbrt`
56×	`associate-*r/`
52×	`associate-/r*` `add-cbrt-cube`
30×	`pow1`
27×	`cbrt-unprod`
26×	`associate-/l*`
17×	`pow-prod-down`
15×	`*-commutative`
7×	`cbrt-undiv` `div-inv`
6×	`clear-num`
4×	`frac-2neg` `un-div-inv` `add-log-exp`
2×	`pow-flip`
1×	`inv-pow`

Counts

4 → 15601

Calls

4 calls:

20.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
639.0ms	(* (* (* (cos k) l) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2))))
7.0ms	(/ (pow l 1) (pow (sin k) 2))
108.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

334.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
387.0ms	(* (* (* (cos k) l) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2))))
71.0ms	(/ (pow l 1) (pow (sin k) 2))
440.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

simplify4.9s

Algorithm

egg-herbie

Counts

15613 → 15613

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	8988	532852

prune1.1m

Filtered

15613 candidates to 8498 candidates (54.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	15602	11	15613
Fresh	13	6	19
Picked	1	0	1
Done	0	0	0
Total	15616	17	15633

Merged error: 0.3b

Counts

15633 → 17

regimes478.0ms

Accuracy

12.9% (3.8b remaining)

Error of 4.0b against oracle of 0.2b and baseline of 4.6b

bsearch273.0ms

Steps

Iters	Range		Point
6	1.0418287907711792e+106	8.525507861768035e+106	2.8947889996786224e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	51
1	60	51
2	60	51

end0.0ms

sample13.1s

Algorithm

intervals

Results

4.1s	2158×	body	2560	valid
3.9s	898×	body	5120	valid
2.9s	4018×	body	1280	valid
1.2s	2495×	body	640	valid
331.0ms	1023×	body	320	valid
230.0ms	1985×	body	80	valid
97.0ms	431×	body	160	valid