Details

sample200.0ms

Algorithm

intervals

Results

95.0ms	81×	body	1280	valid
30.0ms	65×	body	640	valid
27.0ms	264×	body	80	valid
12.0ms	36×	body	320	valid
2.0ms	13×	body	160	valid

simplify194.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	126	13
7	142	13
done	142	13

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 87

Calls

2 calls:

51.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
13.0ms	(/ (cos th) (sqrt 2.0))

series421.0ms

Counts

2 → 6

Calls

2 calls:

305.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
116.0ms	(/ (cos th) (sqrt 2.0))

simplify2.1s

Counts

93 → 93

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	153	1370
1	518	1320
2	2985	1196
done	5000	1191

prune399.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (+ (* a1 a1) (* a2 a2)) (cos th))
0.4b	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`pow1` `associate-*l/`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 49

Calls

2 calls:

41.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
28.0ms	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

series351.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
235.0ms	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

simplify1.6s

Counts

55 → 55

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	107	888
1	283	854
2	1794	726
done	5001	726

prune226.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt 2.0) (cos th))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
92×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
25×	`associate-/r*`
9×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
1×	`flip3-+` `associate-/r/` `flip-+`

Counts

2 → 147

Calls

2 calls:

14.0ms	(/ (sqrt 2.0) (cos th))
70.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series314.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (sqrt 2.0) (cos th))
254.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.2s

Counts

153 → 153

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	240	3357
1	634	3183
2	3962	3052
done	5000	3046

prune620.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt 2.0) (cos th))
0.3b	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
6.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
150×	`sqrt-prod`
28×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `div-inv`
6×	`pow1` `sqrt-div`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/`
1×	`associate-/l/`

Counts

4 → 246

Calls

4 calls:

12.0ms	(/ (sqrt 2.0) (cos th))
45.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
12.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (sqrt 2.0) (cos th))
155.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
47.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
60.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify1.7s

Counts

258 → 258

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	301	6190
1	710	5612
2	2932	5497
done	5001	5490

prune976.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes214.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	16	27
1	20	25
2	22	23
done	22	23

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.8s	2557×	body	1280	valid
1.7s	8014×	body	80	valid
1.6s	2046×	body	640	valid
348.0ms	1016×	body	320	valid
150.0ms	490×	body	160	valid