Details

sample1.0s

Algorithm

intervals

Results

312.0ms	125×	body	1280	valid
278.0ms	42×	body	5120	valid
251.0ms	80×	body	2560	valid
92.0ms	83×	body	640	valid
25.0ms	34×	body	320	valid
13.0ms	60×	body	80	valid
5.0ms	14×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3734
3	704
2	144
1	44
0	19

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 2.0 (pow (/ k t) 2.0))
5.2b	(/ (* l l) (* (sin k) (tan k)))
13.1b	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
33.7b	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

rewrite718.0ms

Algorithm

rewrite-expression-head

Rules

9211×	`times-frac`
3212×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2953×	`unpow-prod-down`
656×	`div-inv`
491×	`sqr-pow`
467×	`add-exp-log`
459×	`associate-/r/`
401×	`tan-quot` `associate-*r/`
331×	`div-exp`
92×	`add-cbrt-cube`
76×	`prod-exp`
71×	`associate-/r*`
66×	`associate-/l*`
64×	`pow-exp`
50×	`cbrt-undiv`
47×	`pow-to-exp`
16×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

4 → 2993

Calls

4 calls:

20.0ms	(/ 2.0 (pow (/ k t) 2.0))
17.0ms	(/ (* l l) (* (sin k) (tan k)))
22.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
135.0ms	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ 2.0 (pow (/ k t) 2.0))
232.0ms	(/ (* l l) (* (sin k) (tan k)))
511.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
1.0s	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

simplify6.7s

Counts

3005 → 3005

Iterations

Iter	Nodes
done	5069
0	5069

prune39.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.7b	(* (pow t 1.0) (pow k 2.0))
16.5b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite245.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 608

Calls

4 calls:

28.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
27.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
31.0ms	(* (pow t 1.0) (pow k 2.0))
93.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.7s

Counts

4 → 12

Calls

4 calls:

584.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
135.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
939.0ms	(* (pow t 1.0) (pow k 2.0))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.5s

Counts

620 → 620

Iterations

Iter	Nodes
done	5002
2	3107
1	1170
0	445

prune1.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.7b

localize90.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.7b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.5b	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite590.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`*-un-lft-identity` `add-cube-cbrt`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-r/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1468

Calls

4 calls:

6.0ms	(pow (sin k) 2)
67.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
179.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (sin k) 2)
533.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
123.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.8s

Counts

1480 → 1480

Iterations

Iter	Nodes
done	5035
2	3649
1	1607
0	582

prune1.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 7.9b

localize86.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
5.4b	(/ (* (sin k) (sin k)) (* (* l l) (cos k)))
6.2b	(/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (sin k) (sin k)) (* (* l l) (cos k))))
10.0b	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (sin k) (sin k)) (* (* l l) (cos k)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

16036×	`add-exp-log`
8808×	`prod-exp`
8458×	`div-exp`
7277×	`pow-exp`
2585×	`pow-to-exp`
1574×	`rec-exp` `1-exp`
632×	`times-frac`
418×	`unpow-prod-down`
311×	`add-sqr-sqrt`
243×	`*-un-lft-identity`
234×	`add-cube-cbrt`
150×	`associate-r`
97×	`add-cbrt-cube`
75×	`div-inv`
64×	`sqr-pow`
36×	`cbrt-unprod`
34×	`cbrt-undiv`
33×	`associate-/l*`
30×	`unswap-sqr`
11×	`associate-l`
7×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`div-sub` `associate-r/` `-commutative` `sqr-sin` `pow-flip` `sin-mult` `inv-pow` `associate-/l/`

Counts

4 → 3380

Calls

4 calls:

18.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
35.0ms	(/ (* (sin k) (sin k)) (* (* l l) (cos k)))
104.0ms	(/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (sin k) (sin k)) (* (* l l) (cos k))))
288.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (sin k) (sin k)) (* (* l l) (cos k)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

530.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
92.0ms	(/ (* (sin k) (sin k)) (* (* l l) (cos k)))
484.0ms	(/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (sin k) (sin k)) (* (* l l) (cos k))))
992.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (sin k) (sin k)) (* (* l l) (cos k)))))

simplify7.2s

Counts

3392 → 3392

Iterations

Iter	Nodes
done	5017
1	4371
0	1857

prune5.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 6.9b

regimes1.5s

Accuracy

38.6% (5.4b remaining)

Error of 11.0b against oracle of 5.6b and baseline of 14.4b

bsearch4.0ms

simplify30.0ms

Iterations

Iter	Nodes
done	80
1	80
0	67

end0.0ms

sample30.6s

Algorithm

intervals

Results

8.6s	3989×	body	1280	valid
8.2s	2317×	body	2560	valid
7.5s	932×	body	5120	valid
3.5s	2554×	body	640	valid
1.2s	1985×	body	80	valid
754.0ms	977×	body	320	valid
235.0ms	421×	body	160	valid