Details

sample142.0ms

Algorithm

intervals

Results

56.0ms	70×	body	1280	valid
31.0ms	60×	body	640	valid
24.0ms	193×	body	80	valid
10.0ms	28×	body	320	valid
3.0ms	12×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	13
1	158	13
2	903	13
3	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.1b	(* (/ (pow t 3.0) (* l l)) (sin k))
11.5b	(* (* (* (/ (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))

rewrite360.0ms

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×	`flip3-+` `flip-+` `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 → 144

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))
298.0ms	(* (* (* (/ (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:

317.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
244.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
624.0ms	(* (* (* (/ (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))

simplify118.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	801	1619
1	4646	1348
2	5002	1348

prune497.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.3b

localize30.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.3b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.5b	(* (* (* (/ (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))

rewrite568.0ms

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×	`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 → 229

Calls

4 calls:

79.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
20.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
453.0ms	(* (* (* (/ (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:

367.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
245.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
200.0ms	(/ (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))

simplify60.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1347	3795
1	5001	3312

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.7b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.5b	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (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

1050×	`add-exp-log`
734×	`prod-exp`
255×	`div-exp`
151×	`add-cbrt-cube`
145×	`pow-to-exp` `pow-exp`
96×	`cbrt-unprod`
47×	`associate-*l/`
40×	`add-sqr-sqrt`
37×	`associate-l`
35×	`frac-times`
34×	`pow1` `times-frac`
33×	`associate-*r/`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
20×	`unpow-prod-down` `pow-prod-down`
19×	`cbrt-undiv`
16×	`tan-quot`
12×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `div-inv`

Counts

4 → 366

Calls

4 calls:

45.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
162.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
782.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

293.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
366.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
242.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
756.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1479	6579
1	5001	5389

prune975.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
1.3b	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.7b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

1049×	`add-exp-log`
733×	`prod-exp`
255×	`div-exp`
149×	`add-cbrt-cube`
146×	`pow-to-exp` `pow-exp`
95×	`cbrt-unprod`
41×	`add-sqr-sqrt`
36×	`associate-l`
34×	`times-frac` `associate-*r/`
33×	`pow1`
30×	`frac-times`
29×	`associate-*l/`
28×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down`
19×	`cbrt-undiv` `pow-prod-down`
13×	`cbrt-prod`
12×	`tan-quot`
8×	`flip3-+` `flip-+`
5×	`associate-r` `unswap-sqr` `sqr-pow`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`pow-pow`
1×	`pow1/3` `div-inv`

Counts

4 → 363

Calls

4 calls:

2.0ms	(pow (cbrt t) 3.0)
45.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
19.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
337.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

307.0ms	(pow (cbrt t) 3.0)
287.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
245.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
745.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1515	6755
1	5001	5848

prune1.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.2b

regimes616.0ms

Accuracy

8.2% (6.7b remaining)

Error of 16.6b against oracle of 9.9b and baseline of 17.2b

bsearch598.0ms

Steps

Iters	Range		Point
7	1.9907280099952322e+102	2.7122260838251684e+104	2.146339439987722e+102
8	3.6262409097193804e-147	2.133881468323433e-144	3.8502617433270982e-146
8	-2.3555604230285885e-90	-8.86136706679591e-93	-1.541434043089921e-91
10	-2.771665303262814e+161	-1.6259263967015282e+146	-3.672920003767779e+146

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	148
1	92	148

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2071×	body	1280	valid
949.0ms	1768×	body	640	valid
686.0ms	5961×	body	80	valid
320.0ms	844×	body	320	valid
108.0ms	432×	body	160	valid