Details

sample229.0ms

Algorithm

intervals

Results

78.0ms	62×	body	1280	valid
52.0ms	183×	body	80	valid
49.0ms	57×	body	640	valid
17.0ms	27×	body	320	valid
6.0ms	16×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	903
2	161
1	48
0	19

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.3b

localize72.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
4.8b	(/ (pow t 3.0) l)
11.8b	(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
17.7b	(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

614×	`times-frac`
245×	`add-sqr-sqrt`
240×	`*-un-lft-identity` `add-cube-cbrt`
157×	`add-exp-log`
94×	`add-cbrt-cube`
93×	`unpow-prod-down`
90×	`associate-/l*`
87×	`div-exp`
85×	`associate-l`
45×	`cbrt-undiv`
37×	`prod-exp`
31×	`sqr-pow`
23×	`cbrt-unprod`
17×	`div-inv`
13×	`associate-r`
7×	`pow-to-exp` `associate-/r*` `pow-exp`
6×	`pow1`
5×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`tan-quot` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 417

Calls

4 calls:

7.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
13.0ms	(/ (pow t 3.0) l)
43.0ms	(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
119.0ms	(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.0s

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
253.0ms	(/ (pow t 3.0) l)
602.0ms	(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
1.0s	(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify2.5s

Counts

429 → 429

Iterations

Iter	Nodes
done	5000
1	2324
0	752

prune3.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.1b

localize134.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
5.2b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
6.4b	(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
12.8b	(* (/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

3721×	`times-frac`
2395×	`add-exp-log`
1741×	`add-sqr-sqrt`
1543×	`*-un-lft-identity` `add-cube-cbrt`
1482×	`cbrt-prod`
1380×	`div-exp`
1218×	`associate-l`
812×	`prod-exp`
673×	`unpow-prod-down`
448×	`add-cbrt-cube`
316×	`cbrt-undiv`
195×	`cbrt-unprod`
158×	`pow-exp`
125×	`sqr-pow`
100×	`pow-to-exp`
40×	`div-inv` `unswap-sqr`
19×	`associate-/l*`
14×	`associate-r`
11×	`pow1` `associate-/r/`
6×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `associate-/r` `pow-prod-down` `associate-l/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`tan-quot` `associate-/l/`

Counts

4 → 1788

Calls

4 calls:

649.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
14.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
30.0ms	(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
460.0ms	(* (/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

series3.5s

Counts

4 → 12

Calls

4 calls:

930.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
702.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
651.0ms	(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
1.2s	(* (/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

simplify3.8s

Counts

1800 → 1800

Iterations

Iter	Nodes
done	5001
0	1804

prune26.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 13.2b

localize163.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.6b	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
4.3b	(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
5.5b	(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

rewrite4.7s

Algorithm

rewrite-expression-head

Rules

13777×	`add-exp-log`
8461×	`div-exp`
7694×	`times-frac`
4576×	`prod-exp`
3453×	`cbrt-prod`
3313×	`add-sqr-sqrt`
3115×	`*-un-lft-identity` `add-cube-cbrt`
2643×	`associate-l`
1561×	`add-cbrt-cube`
1405×	`cbrt-undiv`
930×	`pow-exp`
922×	`cbrt-unprod`
916×	`unpow-prod-down`
564×	`pow-to-exp`
368×	`sqr-pow`
75×	`div-inv`
40×	`unswap-sqr`
23×	`frac-times` `associate-*r/`
20×	`pow1`
15×	`associate-r`
11×	`associate-*l/` `associate-/r/`
10×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
1×	`clear-num` `frac-2neg` `tan-quot`

Counts

4 → 4390

Calls

4 calls:

8.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
740.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
2.0s	(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
881.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

series3.2s

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
938.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
1.1s	(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
1.1s	(* (/ (/ (cbrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

simplify7.9s

Counts

4402 → 4402

Iterations

Iter	Nodes
done	5000
0	3486

prune1.0m

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 12.4b

localize310.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ 1 (* (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt (fma 2 1.0 (pow (/ k t) 2.0))))))
16.5b	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
16.5b	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
16.5b	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite920.0ms

Algorithm

rewrite-expression-head

Rules

3601×	`times-frac`
1735×	`add-sqr-sqrt`
1512×	`cbrt-prod`
1508×	`*-un-lft-identity`
1488×	`add-cube-cbrt`
1172×	`associate-l`
672×	`unpow-prod-down`
195×	`add-exp-log`
120×	`sqr-pow`
108×	`div-exp`
60×	`prod-exp` `unswap-sqr`
41×	`add-cbrt-cube`
26×	`cbrt-undiv`
23×	`div-inv`
16×	`cbrt-unprod`
12×	`rec-exp` `1-exp`
7×	`pow-to-exp` `associate-r` `pow-exp`
6×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 1347

Calls

4 calls:

659.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ 1 (* (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt (fma 2 1.0 (pow (/ k t) 2.0))))))
2.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
1.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
1.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

977.0ms	(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ 1 (* (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt (fma 2 1.0 (pow (/ k t) 2.0))))))
177.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
199.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
216.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

simplify4.6s

Counts

1359 → 1359

Iterations

Iter	Nodes
done	5000
1	4277
0	1256

prune27.6s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 12.4b

regimes3.2s

Accuracy

0% (1.3b remaining)

Error of 12.2b against oracle of 10.9b and baseline of 12.2b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	50
1	50
0	43

end0.0ms

sample9.4s

Algorithm

intervals

Results

3.9s	2026×	body	1280	valid
2.8s	1748×	body	640	valid
1.5s	5830×	body	80	valid
672.0ms	834×	body	320	valid
175.0ms	407×	body	160	valid