Details

sample143.0ms

Algorithm

intervals

Results

48.0ms	62×	body	1280	valid
33.0ms	64×	body	640	valid
21.0ms	200×	body	80	valid
9.0ms	25×	body	320	valid
6.0ms	25×	body	160	valid

simplify32.0ms

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: 29.2b

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.2b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.3b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.3b	(/ (pow t 3.0) (* l l))

rewrite609.0ms

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:

74.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
31.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
486.0ms	(* (* (* (/ (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))

series1.4s

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
253.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
652.0ms	(* (* (* (/ (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))

simplify121.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (23.0ms)

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

prune540.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.6b

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
3.2b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
4.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.3b	(* (* (* (* (/ (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))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

346×	`add-exp-log`
203×	`prod-exp`
97×	`div-exp`
82×	`add-cbrt-cube`
55×	`associate-*l/`
46×	`cbrt-unprod`
41×	`pow-exp`
35×	`frac-times`
32×	`pow1`
28×	`pow-to-exp`
22×	`*-un-lft-identity`
19×	`pow-prod-down`
17×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`tan-quot`
15×	`times-frac` `associate-*r/`
13×	`cbrt-undiv`
11×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`associate-/l*`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`associate-l` `associate-/r` `-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv`

Counts

4 → 212

Calls

4 calls:

177.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
52.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
9.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
878.0ms	(* (* (* (* (/ (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))

series1.6s

Counts

4 → 12

Calls

4 calls:

373.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
293.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
199.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
749.0ms	(* (* (* (* (/ (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))

simplify63.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1196	3855
1	5001	3336

prune778.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
3.0b	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
3.2b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k))
12.3b	(* (* (* (* (* (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))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

891×	`add-exp-log`
622×	`prod-exp`
225×	`div-exp`
124×	`pow-to-exp` `pow-exp`
119×	`add-cbrt-cube`
76×	`cbrt-unprod`
55×	`associate-*l/`
35×	`frac-times`
33×	`pow1` `associate-*r/`
19×	`pow-prod-down`
16×	`tan-quot`
15×	`cbrt-undiv` `*-un-lft-identity`
11×	`associate-r`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`flip3-+` `flip-+`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `associate-l` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `sqr-pow`

Counts

4 → 297

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
626.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
169.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k))
2.7s	(* (* (* (* (* (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:

302.0ms	(pow (cbrt t) 3.0)
368.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
287.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k))
743.0ms	(* (* (* (* (* (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))

simplify282.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1353	5548
1	5002	4690

prune694.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
3.0b	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
3.2b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k))
12.3b	(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

891×	`add-exp-log`
622×	`prod-exp`
225×	`div-exp`
124×	`pow-to-exp` `pow-exp`
119×	`add-cbrt-cube`
76×	`cbrt-unprod`
55×	`associate-*l/`
35×	`frac-times`
33×	`pow1` `associate-*r/`
19×	`pow-prod-down`
16×	`tan-quot`
15×	`cbrt-undiv` `*-un-lft-identity`
11×	`associate-r`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`flip3-+` `flip-+`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `associate-l` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `sqr-pow`

Counts

4 → 297

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
609.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
165.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k))
2.6s	(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

305.0ms	(pow (cbrt t) 3.0)
459.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
376.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k))
867.0ms	(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1408	5506
1	5001	4502

prune774.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

regimes519.0ms

Accuracy

8.5% (6.0b remaining)

Error of 17.5b against oracle of 11.4b and baseline of 18.0b

bsearch574.0ms

Steps

Iters	Range		Point
9	2.2830925651785564e+121	3.970733553694869e+126	5.548140519913771e+121
7	1.885977771534805e-140	9.907707726953698e-139	2.2970494286072416e-139
5	-35564505.319161475	-15359524.008108458	-25217102.05555651
9	-7.727081080122102e+128	-2.5235603851341353e+122	-2.4842396960054388e+123

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	124
1	114	124

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2021×	body	1280	valid
955.0ms	1809×	body	640	valid
646.0ms	5983×	body	80	valid
323.0ms	865×	body	320	valid
129.0ms	481×	body	160	valid