Details

sample495.0ms

Algorithm

intervals

Results

187.0ms	37×	body	5120	valid
122.0ms	69×	body	2560	valid
101.0ms	129×	body	1280	valid
43.0ms	90×	body	640	valid
9.0ms	26×	body	320	valid
6.0ms	56×	body	80	valid
5.0ms	20×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11

prune11.0ms

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: 39.2b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
20.6b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.5b	(* (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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `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 → 187

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
18.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
12.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ k t) 2.0)
233.0ms	(* (pow t 3.0) (tan k))
373.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
254.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify43.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune451.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	190	9	199
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	192	9	201

Merged error: 21.7b

Counts

201 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b	(* (pow k 2.0) (pow t 1.0))
15.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 608

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
25.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
330.0ms	(* (pow k 2.0) (pow t 1.0))
640.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify156.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1439	7252
1	4296	7083
2	5003	7076

prune623.0ms

Filtered

620 candidates to 108 candidates (17.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	609	11	620
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	616	13	629

Merged error: 16.8b

Counts

629 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.9b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.0b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite479.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1468

Calls

4 calls:

3.0ms	(pow (sin k) 2)
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
248.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin k) 2)
332.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
649.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify308.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1997	23615
1	4854	19182
2	5002	17933

prune558.0ms

Filtered

1480 candidates to 94 candidates (6.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	1473	7	1480
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	1478	15	1493

Merged error: 14.4b

Counts

1493 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos k) (sin k))
0.9b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.5b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
15.0b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 939

Calls

4 calls:

4.0ms	(/ (cos k) (sin k))
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
21.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
35.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (cos k) (sin k))
338.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
81.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
661.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify176.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2402	15175
1	5001	12337

prune705.0ms

Filtered

951 candidates to 143 candidates (15.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	943	8	951
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	949	17	966

Merged error: 9.1b

Counts

966 → 17

regimes450.0ms

Accuracy

53.8% (3.3b remaining)

Error of 12.1b against oracle of 8.9b and baseline of 15.9b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	36
1	55	36

end0.0ms

sample13.6s

Algorithm

intervals

Results

4.2s	2183×	body	2560	valid
4.0s	971×	body	5120	valid
3.0s	4019×	body	1280	valid
1.2s	2510×	body	640	valid
345.0ms	1026×	body	320	valid
246.0ms	2047×	body	80	valid
94.0ms	417×	body	160	valid