Details

sample141.0ms

Algorithm

intervals

Results

53.0ms	67×	body	1280	valid
34.0ms	66×	body	640	valid
22.0ms	184×	body	80	valid
9.0ms	24×	body	320	valid
4.0ms	17×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (29.0ms)

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: 33.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.9b	(* (/ (pow t 3.0) (* l l)) (sin k))
15.3b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.4b	(/ (pow t 3.0) (* l l))

rewrite339.0ms

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:

35.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
279.0ms	(* (* (* (/ (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:

322.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
242.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
632.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
181.0ms	(/ (pow t 3.0) (* l l))

simplify117.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (21.0ms)

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

prune527.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.7b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.1b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.3b	(* (* (* (/ (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))

rewrite539.0ms

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))
17.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
427.0ms	(* (* (* (/ (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:

362.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
231.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
194.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
727.0ms	(* (* (* (/ (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))

simplify66.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1364	3882
1	5001	3394

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.4b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.3b	(* (* (* (/ (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:

118.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
161.0ms	(* (* (/ (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))
762.0ms	(* (* (* (/ (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:

278.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
351.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
233.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
922.0ms	(* (* (* (/ (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))

simplify144.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2745	11522
1	5002	10788

prune3.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.1b

localize33.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
2.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.4b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
12.3b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite863.0ms

Algorithm

rewrite-expression-head

Rules

745×	`add-exp-log`
479×	`prod-exp`
210×	`div-exp`
142×	`add-cbrt-cube`
79×	`cbrt-unprod`
75×	`pow-to-exp` `pow-exp`
40×	`add-sqr-sqrt`
36×	`associate-l`
35×	`times-frac`
32×	`*-un-lft-identity`
30×	`cbrt-undiv`
27×	`add-cube-cbrt`
20×	`unpow-prod-down`
18×	`associate-*l/`
13×	`pow1`
11×	`associate-r/` `associate-r*`
10×	`cbrt-prod`
5×	`pow-prod-down` `associate-/l/` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 272

Calls

4 calls:

68.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
19.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
347.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
407.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
237.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
720.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
544.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1375	5522
1	5001	4850

prune869.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.8b

regimes557.0ms

Accuracy

57.8% (3.4b remaining)

Error of 10.0b against oracle of 6.7b and baseline of 14.7b

bsearch342.0ms

Steps

Iters	Range		Point
8	1.2933449595653626e-98	7.481821374969571e-94	7.038206094247466e-94
9	-9.127252329979389e-38	-1.0065887974632998e-42	-5.558092964101593e-38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	49
1	65	49

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2031×	body	1280	valid
958.0ms	1769×	body	640	valid
656.0ms	5882×	body	80	valid
330.0ms	872×	body	320	valid
106.0ms	412×	body	160	valid