Details

sample469.0ms

Algorithm

intervals

Results

175.0ms	78×	body	2560	valid
129.0ms	27×	body	5120	valid
84.0ms	111×	body	1280	valid
41.0ms	88×	body	640	valid
9.0ms	26×	body	320	valid
8.0ms	74×	body	80	valid
3.0ms	12×	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

prune11.0ms

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: 40.6b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
20.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite447.0ms

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)
7.0ms	(* (pow t 3.0) (tan k))
104.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
20.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series936.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ k t) 2.0)
238.0ms	(* (pow t 3.0) (tan k))
375.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
257.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify548.0ms

Algorithm

egg-herbie

Counts

2601 → 2601

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5001	53883

prune7.7s

Filtered

2601 candidates to 1663 candidates (36.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	2579	22	2601
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	2581	22	2603

Merged error: 14.0b

Counts

2603 → 22

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.2b	(* (pow k 2.0) (pow t 1.0))
16.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite477.0ms

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:

16.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0ms	(* (pow k 2.0) (pow t 1.0))
237.0ms	(* (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:

367.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
95.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
353.0ms	(* (pow k 2.0) (pow t 1.0))
671.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify351.0ms

Algorithm

egg-herbie

Counts

1640 → 1640

Iterations

Useful iterations: 1 (85.0ms)

Iter	Nodes	Cost
0	4705	28157
1	5001	26518

prune3.0s

Filtered

1640 candidates to 553 candidates (66.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1624	16	1640
Fresh	13	8	21
Picked	1	0	1
Done	0	0	0
Total	1638	24	1662

Merged error: 5.9b

Counts

1662 → 24

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (pow l (/ 2 2)) (pow (sin k) 2))
3.4b	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
6.2b	(* (pow k 2.0) (pow t 1.0))
7.3b	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

rewrite567.0ms

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:

11.0ms	(/ (pow l (/ 2 2)) (pow (sin k) 2))
205.0ms	(* (* (* (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:

75.0ms	(/ (pow l (/ 2 2)) (pow (sin k) 2))
406.0ms	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
337.0ms	(* (pow k 2.0) (pow t 1.0))
287.0ms	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

simplify388.0ms

Algorithm

egg-herbie

Counts

1906 → 1906

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	39193

prune3.8s

Filtered

1906 candidates to 655 candidates (65.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	1893	13	1906
Fresh	17	6	23
Picked	1	0	1
Done	0	0	0
Total	1911	19	1930

Merged error: 1.9b

Counts

1930 → 19

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
0.9b	(* (* (* (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))
5.4b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

rewrite4.6s

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:

21.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
694.0ms	(* (* (* (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))))
8.0ms	(/ (pow l 1) (pow (sin k) 2))
120.0ms	(* (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:

335.0ms	(/ 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))))
66.0ms	(/ (pow l 1) (pow (sin k) 2))
439.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

simplify5.3s

Algorithm

egg-herbie

Counts

15613 → 15613

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	8988	532848

prune59.6s

Filtered

15613 candidates to 8498 candidates (45.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	15602	11	15613
Fresh	11	7	18
Picked	1	0	1
Done	0	0	0
Total	15614	18	15632

Merged error: 0.0b

Counts

15632 → 18

regimes380.0ms

Accuracy

32.5% (2.2b remaining)

Error of 2.5b against oracle of 0.3b and baseline of 3.6b

bsearch496.0ms

Steps

Iters	Range		Point
8	1.7784932289504506e+23	7.64151557602382e+27	3.191494584105402e+25
8	-3.5719541234060284e-283	-5.934145880640266e-288	-3.505324626283498e-283

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	47
1	60	47
2	60	47

end0.0ms

sample13.8s

Algorithm

intervals

Results

4.5s	2275×	body	2560	valid
3.8s	914×	body	5120	valid
3.0s	4076×	body	1280	valid
1.2s	2554×	body	640	valid
324.0ms	972×	body	320	valid
243.0ms	2113×	body	80	valid
104.0ms	410×	body	160	valid