Details

sample528.0ms

Algorithm

intervals

Results

178.0ms	40×	body	5120	valid
174.0ms	86×	body	2560	valid
93.0ms	132×	body	1280	valid
43.0ms	82×	body	640	valid
7.0ms	21×	body	320	valid
6.0ms	61×	body	80	valid
4.0ms	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

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: 40.0b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.3b	(* (pow t 3.0) (tan k))
18.9b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
31.1b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite55.0ms

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:

8.0ms	(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)))

series939.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ k t) 2.0)
251.0ms	(* (pow t 3.0) (tan k))
374.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
247.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify43.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune445.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	195	6	201

Merged error: 19.6b

Counts

201 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.2b	(* (pow k 2.0) (pow t 1.0))
14.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 575

Calls

4 calls:

3.0ms	(pow (sin k) 2)
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
22.0ms	(* (pow (/ 1 (* (pow k 2.0) (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)
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
341.0ms	(* (pow k 2.0) (pow t 1.0))
679.0ms	(* (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

587 → 587

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1304	6971
1	3873	6815
2	5003	6814

prune611.0ms

Filtered

587 candidates to 104 candidates (17.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	576	11	587
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	579	14	593

Merged error: 14.7b

Counts

593 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b	(pow (sin k) 2)
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.0b	(* (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)))

rewrite280.0ms

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:

12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.0ms	(pow (sin k) 2)
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms	(* (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:

347.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
18.0ms	(pow (sin k) 2)
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
675.0ms	(* (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)))

simplify311.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (98.0ms)

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

prune778.0ms

Filtered

1480 candidates to 95 candidates (6.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	1474	6	1480
Fresh	4	9	13
Picked	0	1	1
Done	0	0	0
Total	1478	16	1494

Merged error: 11.7b

Counts

1494 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (sin k))
0.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.1b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
14.0b	(* (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))))

rewrite201.0ms

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))
13.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
25.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
33.0ms	(* (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:

19.0ms	(/ (cos k) (sin k))
344.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
662.0ms	(* (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))))

simplify182.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2402	15175
1	5001	12337

prune710.0ms

Filtered

951 candidates to 142 candidates (14.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	945	6	951
Fresh	8	6	14
Picked	1	0	1
Done	1	0	1
Total	955	12	967

Merged error: 7.6b

Counts

967 → 12

regimes498.0ms

Accuracy

35.4% (4.6b remaining)

Error of 12.8b against oracle of 8.2b and baseline of 15.3b

bsearch1.1s

Steps

Iters	Range		Point
6	4.062592179265397e+152	3.970566584078497e+153	3.7156081381285796e+153
9	6.404030368164304e-239	1.2444337861141637e-232	2.6367243250483916e-235
11	-1.3978765738910418e-81	-5.4082340853716294e-104	-2.2363941753666618e-92
7	-5.1432851240181534e+154	-3.605266790381871e+152	-2.9921320065094955e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	80
1	78	80

end0.0ms

sample13.4s

Algorithm

intervals

Results

4.2s	2204×	body	2560	valid
3.9s	913×	body	5120	valid
3.0s	4105×	body	1280	valid
1.2s	2462×	body	640	valid
348.0ms	1025×	body	320	valid
223.0ms	1933×	body	80	valid
108.0ms	442×	body	160	valid