Details

sample871.0ms

Algorithm

intervals

Results

243.0ms	79×	body	2560	valid
191.0ms	29×	body	5120	valid
165.0ms	113×	body	1280	valid
82.0ms	32×	body	320	valid
80.0ms	81×	body	640	valid
57.0ms	17×	body	160	valid
14.0ms	61×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	832
2	147
1	44
0	19

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
0.8b	(* (pow (/ k t) 2.0) (tan k))
17.5b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
29.7b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

12307×	`times-frac`
4673×	`add-sqr-sqrt`
4665×	`*-un-lft-identity` `add-cube-cbrt`
1470×	`unpow-prod-down`
954×	`associate-/l*`
487×	`sqr-pow`
358×	`associate-/r*`
350×	`add-exp-log`
328×	`div-inv`
253×	`div-exp`
93×	`associate-/r/`
74×	`add-cbrt-cube`
48×	`prod-exp`
46×	`cbrt-undiv`
45×	`pow-exp`
33×	`pow-to-exp`
17×	`associate-l`
6×	`cbrt-unprod`
4×	`pow1` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`tan-quot` `associate-*r/`
1×	`*-commutative` `associate-/l/`

Counts

4 → 3666

Calls

4 calls:

103.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
46.0ms	(* (pow (/ k t) 2.0) (tan k))
43.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
367.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series1.8s

Counts

4 → 12

Calls

4 calls:

409.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
249.0ms	(* (pow (/ k t) 2.0) (tan k))
363.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
774.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify5.1s

Counts

3678 → 3678

Iterations

Iter	Nodes
done	5342
0	5342

prune44.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.7b

localize81.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.6b	(* (pow t 1.0) (pow k 2.0))
6.8b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.5b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 600

Calls

4 calls:

17.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
15.0ms	(* (pow t 1.0) (pow k 2.0))
14.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
90.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.4s

Counts

4 → 12

Calls

4 calls:

627.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
541.0ms	(* (pow t 1.0) (pow k 2.0))
117.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify4.9s

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1218
0	437

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.5b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.8b	(/ 1 (pow k 2.0))
7.8b	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l))))
12.5b	(/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l)))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

4520×	`add-exp-log`
2317×	`div-exp`
2252×	`prod-exp`
1706×	`pow-exp`
527×	`pow-to-exp`
396×	`rec-exp` `1-exp`
112×	`add-cbrt-cube`
94×	`add-sqr-sqrt`
90×	`times-frac`
67×	`*-un-lft-identity`
64×	`add-cube-cbrt`
55×	`unpow-prod-down`
42×	`associate-l`
41×	`cbrt-undiv` `cbrt-unprod`
21×	`associate-r`
13×	`swap-sqr` `unswap-sqr`
11×	`pow1` `sqr-pow`
8×	`associate-/r*` `div-inv`
6×	`associate-/r/`
4×	`associate-r/` `associate-/l` `add-log-exp`
3×	`frac-times` `associate-*l/`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 1069

Calls

4 calls:

45.0ms	(* (/ (sin k) l) (/ (sin k) l))
15.0ms	(/ 1 (pow k 2.0))
142.0ms	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l))))
48.0ms	(/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ (sin k) l) (/ (sin k) l))
547.0ms	(/ 1 (pow k 2.0))
1.1s	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l))))
500.0ms	(/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l)))

simplify1.9s

Counts

1081 → 1081

Iterations

Iter	Nodes
done	5000
1	2832
0	835

prune2.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 5.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (/ (sin k) l))
0.8b	(/ 1 (pow k 2.0))
5.9b	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
7.7b	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (cos k) (/ (sin k) l))) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

4909×	`add-exp-log`
3183×	`div-exp`
1966×	`pow-exp`
1948×	`times-frac`
1825×	`prod-exp`
930×	`unpow-prod-down`
881×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
607×	`pow-to-exp`
456×	`rec-exp` `1-exp`
382×	`associate-r`
112×	`sqr-pow`
94×	`div-inv`
70×	`add-cbrt-cube`
35×	`associate-/l*`
33×	`associate-/r*`
28×	`cbrt-undiv`
21×	`cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/` `associate-/r/`
1×	`frac-times` `associate-l` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1911

Calls

4 calls:

11.0ms	(/ (cos k) (/ (sin k) l))
12.0ms	(/ 1 (pow k 2.0))
50.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
644.0ms	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (cos k) (/ (sin k) l))) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

series2.1s

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (cos k) (/ (sin k) l))
601.0ms	(/ 1 (pow k 2.0))
379.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
1.0s	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (cos k) (/ (sin k) l))) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

simplify3.1s

Counts

1923 → 1923

Iterations

Iter	Nodes
done	5001
0	1870

prune9.9s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample29.1s

Algorithm

intervals

Results

8.5s	3998×	body	1280	valid
7.9s	2259×	body	2560	valid
7.0s	926×	body	5120	valid
3.2s	2541×	body	640	valid
966.0ms	1034×	body	320	valid
639.0ms	2068×	body	80	valid
235.0ms	421×	body	160	valid