Details

sample869.0ms

Algorithm

intervals

Results

256.0ms	42×	body	5120	valid
235.0ms	131×	body	1280	valid
209.0ms	78×	body	2560	valid
87.0ms	78×	body	640	valid
20.0ms	31×	body	320	valid
15.0ms	77×	body	80	valid
10.0ms	22×	body	160	valid

simplify928.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	856
2	149
1	44
0	19

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
2.3b	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
4.8b	(* (pow t 3.0) (/ (sin k) l))
30.8b	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

575×	`times-frac`
481×	`add-exp-log`
281×	`add-sqr-sqrt`
277×	`div-exp`
243×	`unpow-prod-down`
235×	`*-un-lft-identity` `add-cube-cbrt`
147×	`associate-l`
144×	`prod-exp`
76×	`pow-exp`
68×	`add-cbrt-cube`
57×	`div-inv`
51×	`pow-to-exp`
37×	`associate-*r/`
36×	`associate-/r/`
30×	`cbrt-undiv`
27×	`associate-r`
23×	`sqr-pow`
18×	`cbrt-unprod`
17×	`associate-/r*`
16×	`unswap-sqr`
8×	`associate-/l*`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`*-commutative`
1×	`frac-times` `clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/l/`

Counts

4 → 539

Calls

4 calls:

11.0ms	(pow (/ k t) 2.0)
160.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
29.0ms	(* (pow t 3.0) (/ (sin k) l))
32.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow (/ k t) 2.0)
1.1s	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
279.0ms	(* (pow t 3.0) (/ (sin k) l))
627.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

simplify1.2s

Counts

551 → 551

Iterations

Iter	Nodes
done	5000
1	2534
0	798

prune4.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (tan k))
2.3b	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
7.0b	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
7.9b	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

1087×	`add-exp-log`
540×	`prod-exp`
508×	`div-exp`
370×	`times-frac`
319×	`pow-exp`
190×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
150×	`unpow-prod-down`
139×	`pow-to-exp`
64×	`add-cbrt-cube`
63×	`rec-exp` `1-exp`
50×	`sqr-pow`
28×	`cbrt-unprod` `associate-/l*`
27×	`associate-r`
15×	`cbrt-undiv`
12×	`div-inv`
11×	`pow1`
10×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `tan-quot` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-*l/` `associate-/l/`

Counts

4 → 558

Calls

4 calls:

9.0ms	(/ l (tan k))
1.0s	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
23.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
283.0ms	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))

series2.4s

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ l (tan k))
1.1s	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
503.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
626.0ms	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))

simplify1.5s

Counts

570 → 570

Iterations

Iter	Nodes
done	5000
1	2196
0	764

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (tan k))
0.3b	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
2.3b	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
7.9b	(* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

rewrite7.2s

Algorithm

rewrite-expression-head

Rules

3400×	`add-exp-log`
1957×	`div-exp`
1548×	`prod-exp`
1111×	`pow-exp`
553×	`pow-to-exp`
370×	`times-frac`
190×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
171×	`rec-exp` `1-exp`
150×	`unpow-prod-down`
64×	`add-cbrt-cube`
50×	`sqr-pow`
28×	`cbrt-unprod` `associate-/l*`
27×	`associate-r`
15×	`cbrt-undiv`
12×	`div-inv`
11×	`pow1`
10×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `tan-quot` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-*l/` `associate-/l/`

Counts

4 → 936

Calls

4 calls:

5.0ms	(/ l (tan k))
20.0ms	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
5.5s	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
1.4s	(* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

series2.5s

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ l (tan k))
528.0ms	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
1.2s	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (/ l (tan k)))
598.0ms	(* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

simplify2.0s

Counts

948 → 948

Iterations

Iter	Nodes
done	5001
1	2780
0	926

prune2.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
0.3b	(* l (/ 1 (tan k)))
2.3b	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (* l (/ 1 (tan k))))
7.9b	(* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

rewrite7.5s

Algorithm

rewrite-expression-head

Rules

7532×	`add-exp-log`
4075×	`prod-exp`
3866×	`div-exp`
2203×	`pow-exp`
1087×	`pow-to-exp`
529×	`rec-exp` `1-exp`
363×	`times-frac`
190×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
183×	`add-cube-cbrt`
150×	`unpow-prod-down`
95×	`add-cbrt-cube`
51×	`cbrt-unprod`
50×	`sqr-pow`
28×	`associate-r`
25×	`associate-/l*`
20×	`pow1`
17×	`cbrt-undiv`
11×	`div-inv`
10×	`pow-prod-down`
9×	`associate-*r/`
7×	`associate-/r*`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv` `*-commutative` `unswap-sqr`
2×	`frac-times`
1×	`clear-num` `frac-2neg` `associate-*l/` `tan-quot` `associate-/r/` `associate-/l/`

Counts

4 → 1526

Calls

4 calls:

38.0ms	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
29.0ms	(* l (/ 1 (tan k)))
5.8s	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (* l (/ 1 (tan k))))
1.4s	(* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

series2.5s

Counts

4 → 12

Calls

4 calls:

486.0ms	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
141.0ms	(* l (/ 1 (tan k)))
1.2s	(* (* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k))) (* l (/ 1 (tan k))))
715.0ms	(* (* 2.0 (pow (/ (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))) 1.0)) (/ l (sin k)))

simplify2.2s

Counts

1538 → 1538

Iterations

Iter	Nodes
done	5000
1	3996
0	1140

prune2.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.1b

regimes826.0ms

Accuracy

32.9% (2.6b remaining)

Error of 9.2b against oracle of 6.6b and baseline of 10.5b

bsearch2.5s

Steps

Iters	Range		Point
8	1.501117643472263e+94	1.5380770813396274e+97	1.8513174352851367e+96
8	1.1530756007095177e-28	9.349994741630068e-25	3.616629126787216e-28
5	-8017959488307491.0	-3813544086202141.0	-3851782140446467.0
8	-1.7126502824482385e+73	-2.4653851854550762e+69	-1.6773607976587493e+73

simplify1.1s

Iterations

Iter	Nodes
done	5002
14	2984
13	1849
12	714
11	479
10	244
9	189
8	133
7	108
6	91
5	78
4	72
3	69
2	63
1	60
0	48

end0.0ms

sample32.7s

Algorithm

intervals

Results

9.4s	2227×	body	2560	valid
8.5s	3980×	body	1280	valid
7.4s	981×	body	5120	valid
4.5s	2551×	body	640	valid
968.0ms	1044×	body	320	valid
578.0ms	2011×	body	80	valid
388.0ms	504×	body	160	valid