Details

sample836.0ms

Algorithm

intervals

Results

221.0ms	28×	body	5120	valid
203.0ms	103×	body	1280	valid
194.0ms	65×	body	2560	valid
130.0ms	76×	body	640	valid
38.0ms	43×	body	320	valid
18.0ms	66×	body	80	valid
12.0ms	19×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	1021
2	177
1	51
0	19

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 2 t) (tan k))
1.1b	(/ (* (/ l t) (/ l t)) (sin k))
1.6b	(* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k)))
32.4b	(/ (* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k))) (* (/ k t) (/ k t)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

837×	`add-cbrt-cube` `add-exp-log`
453×	`cbrt-undiv` `div-exp`
260×	`prod-exp` `cbrt-unprod`
157×	`times-frac`
103×	`add-sqr-sqrt`
85×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
15×	`associate-/l*`
12×	`div-inv`
7×	`associate-/r` `associate-r*` `associate-/l/`
6×	`pow1` `unswap-sqr`
5×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`tan-quot`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 427

Calls

4 calls:

11.0ms	(/ (/ 2 t) (tan k))
30.0ms	(/ (* (/ l t) (/ l t)) (sin k))
73.0ms	(* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k)))
85.0ms	(/ (* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k))) (* (/ k t) (/ k t)))

series919.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (/ 2 t) (tan k))
108.0ms	(/ (* (/ l t) (/ l t)) (sin k))
288.0ms	(* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k)))
377.0ms	(/ (* (/ (/ 2 t) (tan k)) (/ (* (/ l t) (/ l t)) (sin k))) (* (/ k t) (/ k t)))

simplify1.5s

Counts

439 → 439

Iterations

Iter	Nodes
done	2001
2	2001
1	1933
0	606

prune6.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.2b

localize53.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* (/ l t) (/ l t)) (sin k))
6.2b	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t)))
12.3b	(/ (/ (/ 2 t) (tan k)) (/ k t))
20.1b	(/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

4259×	`times-frac`
1922×	`add-sqr-sqrt`
1735×	`*-un-lft-identity` `add-cube-cbrt`
784×	`add-cbrt-cube` `add-exp-log`
577×	`associate-l`
507×	`cbrt-undiv` `div-exp`
244×	`div-inv`
159×	`prod-exp` `cbrt-unprod`
96×	`associate-r`
52×	`associate-/l*`
35×	`unswap-sqr`
31×	`associate-/r/`
29×	`associate-/r*`
27×	`tan-quot`
6×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 1744

Calls

4 calls:

17.0ms	(/ (* (/ l t) (/ l t)) (sin k))
127.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t)))
22.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
26.0ms	(/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t))

series836.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* (/ l t) (/ l t)) (sin k))
412.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t)))
164.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
150.0ms	(/ (/ (* (/ l t) (/ l t)) (sin k)) (/ k t))

simplify2.2s

Counts

1756 → 1756

Iterations

Iter	Nodes
done	2416
0	2416

prune29.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.8b

localize77.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (/ l t) (sin k))
8.5b	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (/ l t) 1) 1))
12.3b	(/ (/ (/ 2 t) (tan k)) (/ k t))
13.1b	(/ (/ (/ l t) (sin k)) (/ k t))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

6327×	`times-frac`
2972×	`add-sqr-sqrt`
2625×	`*-un-lft-identity`
2562×	`add-cube-cbrt`
577×	`associate-l`
461×	`add-exp-log`
352×	`div-exp`
318×	`div-inv`
209×	`add-cbrt-cube`
135×	`cbrt-undiv`
133×	`associate-r`
100×	`associate-/l*`
77×	`prod-exp` `unswap-sqr`
63×	`1-exp`
30×	`associate-/r/`
29×	`associate-/r*`
28×	`cbrt-unprod`
27×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 2278

Calls

4 calls:

12.0ms	(/ (/ l t) (sin k))
112.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (/ l t) 1) 1))
32.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
41.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

series644.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (/ l t) (sin k))
231.0ms	(* (/ (/ (/ 2 t) (tan k)) (/ k t)) (/ (/ (/ l t) 1) 1))
163.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
145.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

simplify3.2s

Counts

2290 → 2290

Iterations

Iter	Nodes
done	3469
0	3469

prune41.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.8b

localize163.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (/ (/ 1 (* (cbrt t) (cbrt t))) 1) (/ (* (cbrt k) (cbrt k)) (* (cbrt t) (cbrt t))))
3.5b	(/ (/ l t) (sin k))
5.5b	(* (/ (/ (/ 2 (cbrt t)) (tan k)) (/ (cbrt k) (cbrt t))) (/ (/ (/ l t) 1) 1))
13.1b	(/ (/ (/ l t) (sin k)) (/ k t))

rewrite854.0ms

Algorithm

rewrite-expression-head

Rules

13941×	`times-frac`
6765×	`add-sqr-sqrt`
5548×	`*-un-lft-identity`
5359×	`add-cube-cbrt`
3867×	`cbrt-prod`
2845×	`associate-l`
795×	`add-exp-log`
582×	`div-exp`
402×	`div-inv`
231×	`unswap-sqr`
216×	`add-cbrt-cube`
181×	`cbrt-undiv`
167×	`prod-exp`
133×	`associate-r`
118×	`1-exp`
81×	`associate-/l*`
49×	`cbrt-unprod`
43×	`associate-/r/`
40×	`tan-quot`
21×	`associate-/r*`
20×	`rec-exp`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 4309

Calls

4 calls:

43.0ms	(/ (/ (/ 1 (* (cbrt t) (cbrt t))) 1) (/ (* (cbrt k) (cbrt k)) (* (cbrt t) (cbrt t))))
22.0ms	(/ (/ l t) (sin k))
401.0ms	(* (/ (/ (/ 2 (cbrt t)) (tan k)) (/ (cbrt k) (cbrt t))) (/ (/ (/ l t) 1) 1))
21.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

series790.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ (/ 1 (* (cbrt t) (cbrt t))) 1) (/ (* (cbrt k) (cbrt k)) (* (cbrt t) (cbrt t))))
138.0ms	(/ (/ l t) (sin k))
414.0ms	(* (/ (/ (/ 2 (cbrt t)) (tan k)) (/ (cbrt k) (cbrt t))) (/ (/ (/ l t) 1) 1))
119.0ms	(/ (/ (/ l t) (sin k)) (/ k t))

simplify5.2s

Counts

4321 → 4321

Iterations

Iter	Nodes
done	4388
0	4388

prune1.9m

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.0b

regimes716.0ms

Accuracy

0% (1.5b remaining)

Error of 7.4b against oracle of 5.9b and baseline of 7.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample31.9s

Algorithm

intervals

Results

9.5s	4149×	body	1280	valid
8.0s	2174×	body	2560	valid
6.4s	980×	body	5120	valid
4.5s	2510×	body	640	valid
1.8s	1061×	body	320	valid
770.0ms	2122×	body	80	valid
560.0ms	447×	body	160	valid