Details

sample135.0ms

Algorithm

intervals

Results

54.0ms	62×	body	1280	valid
28.0ms	52×	body	640	valid
22.0ms	198×	body	80	valid
12.0ms	30×	body	320	valid
2.0ms	8×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	48	13
1	161	13
2	944	13
3	5002	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.5b

localize20.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (/ (pow t 3.0) (* l l)) (sin k))
4.1b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
11.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.5b	(/ (pow t 3.0) (* l l))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*`

Counts

4 → 152

Calls

4 calls:

15.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
33.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
287.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms	(/ (pow t 3.0) (* l l))

series1.4s

Counts

4 → 12

Calls

4 calls:

247.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
318.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
622.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
178.0ms	(/ (pow t 3.0) (* l l))

simplify115.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	817	1679
1	4726	1405
2	5001	1405

prune540.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.1b

localize26.0ms

Local error

Found 4 expressions with local error:

4.1b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.4b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.9b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

304×	`add-exp-log`
184×	`prod-exp`
78×	`add-cbrt-cube`
77×	`div-exp`
50×	`add-sqr-sqrt`
49×	`times-frac`
44×	`associate-*l/` `cbrt-unprod`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
36×	`associate-l`
34×	`frac-times`
33×	`pow-exp`
29×	`pow1`
24×	`unpow-prod-down`
22×	`pow-to-exp`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
12×	`cbrt-undiv`
11×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+` `sqr-pow`
5×	`associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 237

Calls

4 calls:

75.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
433.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

359.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
234.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
199.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
729.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1364	3882
1	5001	3394

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
4.1b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.9b	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
437×	`prod-exp`
291×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
63×	`cbrt-unprod`
44×	`associate-*l/`
43×	`add-sqr-sqrt`
36×	`associate-l`
35×	`*-un-lft-identity`
34×	`frac-times` `times-frac`
30×	`pow1` `add-cube-cbrt`
26×	`unpow-prod-down`
25×	`cbrt-undiv`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
13×	`cbrt-prod`
11×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `div-inv`

Counts

4 → 306

Calls

4 calls:

2.0ms	(pow (cbrt t) 3.0)
163.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
804.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

299.0ms	(pow (cbrt t) 3.0)
372.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
235.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
898.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1570	5422
1	5001	4782

prune979.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.0b

localize24.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.5b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
10.0b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite889.0ms

Algorithm

rewrite-expression-head

Rules

576×	`add-exp-log`
347×	`prod-exp`
183×	`div-exp`
128×	`times-frac`
103×	`add-cbrt-cube`
80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
67×	`pow-to-exp` `add-cube-cbrt` `pow-exp`
56×	`unpow-prod-down`
53×	`cbrt-unprod`
36×	`associate-l`
34×	`associate-/r*`
28×	`cbrt-prod` `associate-*l/`
25×	`associate-*r/`
23×	`cbrt-undiv`
19×	`frac-times`
14×	`tan-quot`
13×	`pow1`
11×	`associate-r` `associate-/l/`
10×	`sqr-pow`
8×	`flip3-+` `flip-+`
5×	`pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`*-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 328

Calls

4 calls:

70.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
355.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
419.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

351.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
235.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
716.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
800.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1759	6282
1	5002	5767

prune1.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 6.4b

regimes682.0ms

Accuracy

45.2% (4.1b remaining)

Error of 11.0b against oracle of 7.0b and baseline of 14.4b

bsearch225.0ms

Steps

Iters	Range		Point
10	1.9163617274099722e-113	1.5985324054663707e-103	3.7844580688456216e-104
0	-3.735885180153458e+51	-3.679833018558449e+51	-3.7078590993559536e+51

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	92
1	89	92

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2051×	body	1280	valid
957.0ms	1739×	body	640	valid
700.0ms	5983×	body	80	valid
338.0ms	845×	body	320	valid
106.0ms	415×	body	160	valid