Details

sample136.0ms

Algorithm

intervals

Results

60.0ms	75×	body	1280	valid
27.0ms	50×	body	640	valid
20.0ms	182×	body	80	valid
8.0ms	21×	body	320	valid
4.0ms	18×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.9b	(* (/ (pow t 3.0) (* l l)) (sin k))
15.7b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.2b	(/ (pow t 3.0) (* l l))

rewrite342.0ms

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:

34.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
282.0ms	(* (* (* (/ (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:

329.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
250.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
653.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
185.0ms	(/ (pow t 3.0) (* l l))

simplify181.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (22.0ms)

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

prune534.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.2b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.7b	(* (* (* (/ (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))

rewrite754.0ms

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:

76.0ms	(* (* (/ (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)
640.0ms	(* (* (* (/ (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:

357.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
227.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
193.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
718.0ms	(* (* (* (/ (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))

simplify71.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1364	3882
1	5001	3394

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.2b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.2b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.7b	(* (* (* (/ (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))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1050×	`add-exp-log`
674×	`times-frac`
554×	`prod-exp`
435×	`div-exp`
404×	`unpow-prod-down`
381×	`associate-l`
343×	`add-sqr-sqrt`
335×	`*-un-lft-identity`
330×	`add-cube-cbrt`
202×	`cbrt-prod`
151×	`add-cbrt-cube`
145×	`pow-to-exp` `pow-exp`
78×	`cbrt-unprod`
68×	`sqr-pow`
47×	`associate-*l/`
37×	`cbrt-undiv`
35×	`frac-times`
34×	`pow1`
20×	`pow-prod-down`
16×	`tan-quot`
15×	`associate-*r/`
12×	`associate-r` `div-inv`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`

Counts

4 → 718

Calls

4 calls:

117.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
162.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
777.0ms	(* (* (* (/ (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))

series1.6s

Counts

4 → 12

Calls

4 calls:

283.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
357.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
237.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
737.0ms	(* (* (* (/ (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))

simplify143.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2745	11522
1	5002	10788

prune3.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.3b

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.2b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.3b	(/ (* (* (* (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)))
11.0b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite877.0ms

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:

69.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
353.0ms	(/ (* (* (* (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)))
409.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

359.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
242.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
745.0ms	(/ (* (* (* (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)))
825.0ms	(* (* (* (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 (34.0ms)

Iter	Nodes	Cost
0	1759	6282
1	5002	5767

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 6.7b

regimes662.0ms

Accuracy

53.7% (3.6b remaining)

Error of 10.7b against oracle of 7.1b and baseline of 14.8b

bsearch473.0ms

Steps

Iters	Range		Point
6	3.8604662879896707e-119	3.057994092465889e-118	3.011760324940243e-118
7	-1.6970256405858473e-98	-6.771984168847719e-100	-3.296004383437099e-99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	93
1	83	93

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	2101×	body	1280	valid
944.0ms	1740×	body	640	valid
645.0ms	5904×	body	80	valid
317.0ms	846×	body	320	valid
101.0ms	404×	body	160	valid