Details

sample432.0ms

Algorithm

intervals

Results

132.0ms	58×	body	2560	valid
107.0ms	134×	body	1280	valid
105.0ms	27×	body	5120	valid
49.0ms	83×	body	640	valid
9.0ms	65×	body	80	valid
8.0ms	21×	body	320	valid
4.0ms	15×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

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: 38.3b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
1.0b	(* (pow t 3.0) (tan k))
17.8b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.4b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-exp-log`
265×	`prod-exp`
74×	`div-exp` `add-cbrt-cube`
61×	`pow-exp`
41×	`pow-to-exp`
40×	`cbrt-unprod`
25×	`associate-l`
21×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv`
10×	`times-frac`
7×	`associate-r/` `associate-r*`
6×	`pow1`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `unswap-sqr` `sqr-pow`
2×	`associate-*l/` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 193

Calls

4 calls:

12.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
5.0ms	(* (pow t 3.0) (tan k))
21.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
226.0ms	(* (pow t 3.0) (tan k))
358.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
244.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify137.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	925	2237
1	4805	1854
2	5001	1854

prune412.0ms

Filtered

205 candidates to 88 candidates (42.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	8	205
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	9	207

Merged error: 19.2b

Counts

207 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.3b	(* (pow k 2.0) (pow t 1.0))
13.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite106.0ms

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))
26.0ms	(* (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:

326.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
330.0ms	(* (pow k 2.0) (pow t 1.0))
636.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify164.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (89.0ms)

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

prune616.0ms

Filtered

620 candidates to 108 candidates (17.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	610	10	620
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	616	13	629

Merged error: 15.0b

Counts

629 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
1.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.9b	(* (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)))

rewrite266.0ms

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))
41.0ms	(* (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:

25.0ms	(pow (sin k) 2)
331.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
655.0ms	(* (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)))

simplify304.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (97.0ms)

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

prune581.0ms

Filtered

1480 candidates to 95 candidates (6.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	1472	8	1480
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	1475	18	1493

Merged error: 12.3b

Counts

1493 → 18

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (sin k))
1.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.9b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
13.9b	(* (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))))

rewrite392.0ms

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:

8.0ms	(/ (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)))
31.0ms	(* (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))
333.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
640.0ms	(* (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))))

simplify171.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2402	15175
1	5001	12337

prune709.0ms

Filtered

951 candidates to 142 candidates (14.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	943	8	951
Fresh	13	4	17
Picked	0	1	1
Done	0	0	0
Total	956	13	969

Merged error: 8.7b

Counts

969 → 13

regimes489.0ms

Accuracy

48.4% (4.0b remaining)

Error of 12.8b against oracle of 8.8b and baseline of 16.5b

bsearch1.4s

Steps

Iters	Range		Point
5	2.5993041062962728e+115	5.952677531200359e+115	5.8793295634152445e+115
10	1.2402465223798948e-164	4.419350078268736e-148	4.335363307248357e-148
8	-1.6913487525534787e-78	-4.910609096437828e-82	-7.315155230183912e-79
8	-3.3009884143809787e+109	-2.0290631556484457e+105	-1.6916605671035656e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	87
1	68	87

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.5s	2206×	body	2560	valid
4.0s	950×	body	5120	valid
3.4s	4161×	body	1280	valid
1.3s	2427×	body	640	valid
380.0ms	995×	body	320	valid
279.0ms	2079×	body	80	valid
112.0ms	425×	body	160	valid