Details

sample109.0ms

Algorithm

intervals

Results

34.0ms	77×	body	1280	valid
23.0ms	322×	body	80	valid
20.0ms	62×	body	640	valid
9.0ms	38×	body	320	valid
4.0ms	24×	body	160	valid

simplify13.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	15	7
2	32	7
3	69	7
4	144	7
5	272	7
6	482	7
7	1052	7
8	2094	7
9	3638	7
10	4858	7
done	5000	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.1b	(* (sin x) (sinh y))
14.3b	(/ (* (sin x) (sinh y)) x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`sinh-def` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

1.0ms	(sinh y)
13.0ms	(* (sin x) (sinh y))
19.0ms	(/ (* (sin x) (sinh y)) x)

series394.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sinh y)
156.0ms	(* (sin x) (sinh y))
146.0ms	(/ (* (sin x) (sinh y)) x)

simplify4.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	117	538
1	270	516
2	984	445
3	4845	419
done	5000	419

prune162.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.0b	(/ (sinh y) x)
0.1b	(* (/ (sinh y) x) (sin x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-r` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `sinh-def` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

3 → 68

Calls

3 calls:

3.0ms	(sinh y)
12.0ms	(/ (sinh y) x)
24.0ms	(* (/ (sinh y) x) (sin x))

series374.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(sinh y)
142.0ms	(/ (sinh y) x)
138.0ms	(* (/ (sinh y) x) (sin x))

simplify2.3s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	141	721
1	324	694
2	897	622
3	2878	620
done	5000	620

prune285.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.1b	(* (sinh y) (/ (sin x) x))
0.1b	(/ (sin x) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`sinh-def` `associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 69

Calls

3 calls:

2.0ms	(sinh y)
29.0ms	(* (sinh y) (/ (sin x) x))
10.0ms	(/ (sin x) x)

series278.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(sinh y)
137.0ms	(* (sinh y) (/ (sin x) x))
38.0ms	(/ (sin x) x)

simplify2.8s

Counts

78 → 78

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	134	733
1	299	700
2	999	631
3	3632	629
done	5000	629

prune282.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* 1/6 (pow y 3)) (+ (* 1/120 (pow y 5)) y)) (/ (sin x) x))
0.1b	(* 1/120 (pow y 5))
0.1b	(* 1/6 (pow y 3))
0.1b	(/ (sin x) x)

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
32×	`associate-r`
27×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
19×	`times-frac`
15×	`add-cbrt-cube`
9×	`associate-l` `unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1`
4×	`cube-prod` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `pow-to-exp` `flip3-+` `div-exp` `associate-*l/` `pow-exp` `flip-+` `div-inv`
1×	`cube-mult` `frac-2neg` `unpow3` `associate-*r/` `pow-prod-down` `clear-num`

Counts

4 → 119

Calls

4 calls:

161.0ms	(* (+ (* 1/6 (pow y 3)) (+ (* 1/120 (pow y 5)) y)) (/ (sin x) x))
24.0ms	(* 1/120 (pow y 5))
17.0ms	(* 1/6 (pow y 3))
18.0ms	(/ (sin x) x)

series425.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (+ (* 1/6 (pow y 3)) (+ (* 1/120 (pow y 5)) y)) (/ (sin x) x))
98.0ms	(* 1/120 (pow y 5))
78.0ms	(* 1/6 (pow y 3))
50.0ms	(/ (sin x) x)

simplify1.9s

Counts

131 → 131

Iterations

Useful iterations: 2 (798.0ms)

Iter	Nodes	Cost
0	213	1733
1	516	1611
2	1928	1469
done	5000	1469

prune639.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes102.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	7	7
done	7	7

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	2004×	body	640	valid
1.2s	1811×	body	1280	valid
1.0s	10276×	body	80	valid
287.0ms	1143×	body	320	valid
99.0ms	582×	body	160	valid