Details

sample143.0ms

Algorithm

intervals

Results

60.0ms	69×	body	1280	valid
28.0ms	54×	body	640	valid
23.0ms	208×	body	80	valid
8.0ms	21×	body	320	valid
4.0ms	15×	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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.4b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
18.4b	(/ (pow t 3.0) (* l l))

rewrite603.0ms

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:

73.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
31.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
482.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms	(/ (pow t 3.0) (* l l))

series1.3s

Counts

4 → 12

Calls

4 calls:

304.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
240.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
604.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
176.0ms	(/ (pow t 3.0) (* l l))

simplify120.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (22.0ms)

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

prune548.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize30.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (/ (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))
9.0b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b	(* (* (* (/ (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))

rewrite882.0ms

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:

137.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
29.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
693.0ms	(* (* (* (/ (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:

344.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
225.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
191.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
702.0ms	(* (* (* (/ (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

249 → 249

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1364	3882
1	5001	3394

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
2.5b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (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))
12.9b	(* (* (* (* (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))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
557×	`prod-exp`
171×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
75×	`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` `associate-*r/`
26×	`unpow-prod-down`
17×	`pow-prod-down`
16×	`tan-quot`
13×	`cbrt-undiv` `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:

3.0ms	(pow (cbrt t) 3.0)
259.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
29.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s	(* (* (* (* (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))

series1.8s

Counts

4 → 12

Calls

4 calls:

283.0ms	(pow (cbrt t) 3.0)
546.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
224.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
707.0ms	(* (* (* (* (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

318 → 318

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1530	5382
1	5001	4519

prune1.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
0.7b	(pow (cbrt t) 3.0)
2.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.0b	(* (* (* (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)))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

772×	`add-exp-log`
556×	`prod-exp`
171×	`div-exp`
113×	`add-cbrt-cube`
99×	`pow-to-exp` `pow-exp`
74×	`cbrt-unprod`
44×	`add-sqr-sqrt`
35×	`associate-l`
34×	`times-frac`
32×	`unpow-prod-down`
31×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
29×	`pow1` `frac-times`
26×	`associate-*l/`
16×	`cbrt-prod` `pow-prod-down`
13×	`cbrt-undiv`
12×	`tan-quot`
8×	`flip3-+` `flip-+`
6×	`pow-unpow` `sqr-pow`
5×	`unswap-sqr`
4×	`distribute-rgt-in` `expm1-log1p-u` `pow-pow` `distribute-lft-in` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `*-commutative`
1×	`div-inv`

Counts

4 → 303

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
3.0ms	(pow (cbrt t) 3.0)
29.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
505.0ms	(* (* (* (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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

287.0ms	(pow (cbrt t) 3.0)
291.0ms	(pow (cbrt t) 3.0)
219.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
688.0ms	(* (* (* (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)))

simplify78.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1478	5535
1	5002	4807

prune871.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.7b

regimes623.0ms

Accuracy

8.9% (6.7b remaining)

Error of 16.9b against oracle of 10.1b and baseline of 17.5b

bsearch351.0ms

Steps

Iters	Range		Point
8	2.9338426415425125e-10	4.1138966637094727e-07	7.397929561345073e-10
9	-3.144652509885462e-246	-1.002644781556735e-251	-1.2108300806256563e-247

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	64
1	76	64

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	2149×	body	1280	valid
907.0ms	1636×	body	640	valid
668.0ms	5858×	body	80	valid
327.0ms	884×	body	320	valid
112.0ms	443×	body	160	valid