Details

sample150.0ms

Algorithm

intervals

Results

55.0ms	62×	body	1280	valid
35.0ms	64×	body	640	valid
23.0ms	200×	body	80	valid
10.0ms	25×	body	320	valid
6.0ms	25×	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: 30.3b

localize21.0ms

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))

rewrite651.0ms

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:

78.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
32.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
523.0ms	(* (* (* (/ (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:

331.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
258.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
656.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
188.0ms	(/ (pow t 3.0) (* l l))

simplify118.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (23.0ms)

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

prune472.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.6b

localize30.0ms

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))

rewrite1.2s

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×	`unpow-prod-down` `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 → 204

Calls

4 calls:

193.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
55.0ms	(* (* (/ (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)
963.0ms	(* (* (* (* (/ (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:

377.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
289.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
194.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
748.0ms	(* (* (* (* (/ (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))

simplify56.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1179	3756
1	5001	3242

prune705.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.6b

localize25.0ms

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))

rewrite3.8s

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×	`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 → 289

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
695.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
186.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k))
2.9s	(* (* (* (* (* (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:

298.0ms	(pow (cbrt t) 3.0)
361.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
288.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (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))

simplify67.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1335	5449
1	5001	4596

prune653.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.4b

localize34.0ms

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))

rewrite3.7s

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×	`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 → 289

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
671.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
182.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k))
2.8s	(* (* (* (* (* (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:

297.0ms	(pow (cbrt t) 3.0)
467.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
381.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k))
881.0ms	(* (* (* (* (* (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))

simplify79.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1389	5406
1	5001	4407

prune702.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.4b

regimes792.0ms

Accuracy

8.7% (5.9b remaining)

Error of 17.5b against oracle of 11.5b and baseline of 18.0b

bsearch578.0ms

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

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	125
1	117	125

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	2021×	body	1280	valid
1.0s	1809×	body	640	valid
719.0ms	5983×	body	80	valid
350.0ms	865×	body	320	valid
129.0ms	481×	body	160	valid