Details

sample147.0ms

Algorithm

intervals

Results

55.0ms	314×	body	80	valid
34.0ms	25×	body	1280	valid
26.0ms	35×	body	640	valid
9.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify5.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
6	4062
5	1352
4	542
3	196
2	66
1	28
0	12

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
4.7b	(* sin (* x cos))
4.7b	(* sin (* x cos))

rewrite777.0ms

Algorithm

rewrite-expression-head

Rules

535×	`add-sqr-sqrt`
460×	`associate-r`
262×	`associate-l`
252×	`times-frac`
241×	`*-un-lft-identity`
223×	`unswap-sqr`
201×	`add-cube-cbrt`
130×	`swap-sqr`
128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
84×	`associate-/r*`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
49×	`*-commutative`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-plus` `associate-/l*`
1×	`pow2` `clear-num` `frac-2neg` `div-sub` `cos-2` `div-inv`

Counts

4 → 580

Calls

4 calls:

375.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
269.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
30.0ms	(* sin (* x cos))
46.0ms	(* sin (* x cos))

series302.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
91.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
40.0ms	(* sin (* x cos))
47.0ms	(* sin (* x cos))

simplify1.8s

Counts

592 → 592

Iterations

Iter	Nodes
done	5000
1	2214
0	656

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
4.7b	(* sin (* x cos))
4.7b	(* sin (* x cos))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1813×	`add-sqr-sqrt`
1776×	`times-frac`
1234×	`associate-r`
1018×	`*-un-lft-identity`
903×	`add-cube-cbrt`
715×	`associate-l`
610×	`unswap-sqr`
364×	`swap-sqr`
259×	`associate-/r*`
205×	`add-exp-log`
130×	`*-commutative`
129×	`pow1`
114×	`prod-exp`
109×	`add-cbrt-cube`
90×	`associate-/r/` `associate-/l*`
72×	`pow-prod-down`
60×	`cbrt-unprod`
52×	`div-exp`
21×	`cbrt-undiv`
11×	`rec-exp` `1-exp`
9×	`pow-sqr` `pow-prod-up`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `remove-double-div` `add-log-exp`
3×	`clear-num` `pow-plus`
2×	`frac-2neg`
1×	`pow2` `pow-flip` `inv-pow`

Counts

4 → 1387

Calls

4 calls:

792.0ms	(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
301.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
40.0ms	(* sin (* x cos))
59.0ms	(* sin (* x cos))

series303.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
79.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
42.0ms	(* sin (* x cos))
48.0ms	(* sin (* x cos))

simplify2.8s

Counts

1399 → 1399

Iterations

Iter	Nodes
done	5001
0	1879

prune7.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

4.7b	(* sin (* x cos))
20.4b	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))
20.4b	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))
20.4b	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))

rewrite845.0ms

Algorithm

rewrite-expression-head

Rules

273×	`associate-r`
270×	`add-sqr-sqrt`
252×	`cbrt-prod`
156×	`associate-l`
133×	`unswap-sqr`
95×	`*-un-lft-identity`
78×	`swap-sqr`
71×	`add-cube-cbrt`
29×	`*-commutative`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 319

Calls

4 calls:

53.0ms	(* sin (* x cos))
274.0ms	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))
237.0ms	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))
267.0ms	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* sin (* x cos))
166.0ms	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))
137.0ms	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))
132.0ms	(cbrt (* (* sin (* x cos)) (* sin (* x cos))))

simplify2.5s

Counts

331 → 331

Iterations

Iter	Nodes
done	5010
2	3142
1	777
0	291

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt cos)
0.5b	(cbrt cos)
3.8b	(* sin (* x (* (cbrt cos) (cbrt cos))))
4.7b	(* sin (* x cos))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt` `associate-r`
44×	`unswap-sqr`
34×	`cbrt-prod`
26×	`add-cbrt-cube`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1` `associate-l` `add-exp-log` `cbrt-unprod`
10×	`swap-sqr`
9×	`pow-prod-down` `prod-exp`
7×	`*-commutative`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`

Counts

4 → 142

Calls

4 calls:

1.0ms	(cbrt cos)
1.0ms	(cbrt cos)
224.0ms	(* sin (* x (* (cbrt cos) (cbrt cos))))
33.0ms	(* sin (* x cos))

series1.2s

Counts

4 → 12

Calls

4 calls:

697.0ms	(cbrt cos)
321.0ms	(cbrt cos)
166.0ms	(* sin (* x (* (cbrt cos) (cbrt cos))))
34.0ms	(* sin (* x cos))

simplify1.9s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	2404
1	616
0	218

prune842.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes279.0ms

Accuracy

-38.6% (4.3b remaining)

Error of 4.4b against oracle of 0.1b and baseline of 3.2b

bsearch267.0ms

Steps

Iters	Range		Point
9	-6.265987492454644e-205	-1.9383092559215741e-212	-6.168883927619536e-205

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	23

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	9202×	body	80	valid
1.4s	827×	body	1280	valid
785.0ms	922×	body	640	valid
460.0ms	619×	body	320	valid
124.0ms	326×	body	160	valid