Details

sample193.0ms

Algorithm

intervals

Results

62.0ms	78×	body	640	valid
57.0ms	86×	body	1280	valid
27.0ms	264×	body	80	valid
11.0ms	36×	body	320	valid
5.0ms	23×	body	160	valid

simplify144.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (cos th) (/ (sqrt 2.0) (+ (* a1 a1) (* a2 a2))))
0.4b	(/ (sqrt 2.0) (+ (* a1 a1) (* a2 a2)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
27×	`associate-/r*`
11×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`flip3-+` `flip-+` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

3 → 166

Calls

3 calls:

12.0ms	(+ (* a1 a1) (* a2 a2))
44.0ms	(/ (cos th) (/ (sqrt 2.0) (+ (* a1 a1) (* a2 a2))))
20.0ms	(/ (sqrt 2.0) (+ (* a1 a1) (* a2 a2)))

series452.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* a1 a1) (* a2 a2))
270.0ms	(/ (cos th) (/ (sqrt 2.0) (+ (* a1 a1) (* a2 a2))))
126.0ms	(/ (sqrt 2.0) (+ (* a1 a1) (* a2 a2)))

simplify1.7s

Counts

175 → 175

Iterations

Iter	Nodes
done	5080
2	2152
1	654
0	254

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2))))) (/ (cos th) (/ (cbrt (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))))
0.3b	(/ (cos th) (/ (cbrt (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2)))))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

963×	`times-frac`
638×	`add-sqr-sqrt`
433×	`*-un-lft-identity`
409×	`add-cube-cbrt`
381×	`sqrt-prod`
280×	`cbrt-prod`
185×	`associate-r`
135×	`add-exp-log`
69×	`div-exp`
60×	`associate-/r*`
56×	`unswap-sqr`
52×	`add-cbrt-cube`
41×	`associate-l`
39×	`prod-exp`
30×	`cbrt-undiv`
24×	`sqrt-div`
23×	`associate-/r/`
15×	`cbrt-unprod`
13×	`div-inv`
12×	`flip3-+` `flip-+`
9×	`rec-exp` `1-exp`
8×	`pow1`
4×	`add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 624

Calls

4 calls:

342.0ms	(* (/ 1 (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2))))) (/ (cos th) (/ (cbrt (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))))
41.0ms	(/ (cos th) (/ (cbrt (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2)))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series1000.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (/ 1 (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2))))) (/ (cos th) (/ (cbrt (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))))
638.0ms	(/ (cos th) (/ (cbrt (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2)))))
63.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
52.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify3.2s

Counts

636 → 636

Iterations

Iter	Nodes
done	5001
1	2598
0	733

prune3.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2))))
0.3b	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2)))) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2)))))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `times-frac`
45×	`add-exp-log`
35×	`add-cbrt-cube`
33×	`*-un-lft-identity` `add-cube-cbrt`
31×	`associate-l`
30×	`sqrt-prod`
22×	`cbrt-prod`
19×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
12×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
8×	`pow1` `flip3-+` `flip-+` `unswap-sqr`
6×	`associate-r`
5×	`associate-/r/` `associate-/l/`
4×	`frac-times` `associate-*r/` `div-inv` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 152

Calls

4 calls:

41.0ms	(* (/ (cos th) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2))))
67.0ms	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2)))) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2)))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

638.0ms	(* (/ (cos th) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2))))
302.0ms	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2)))) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (* a1 a1) (* a2 a2)))))
65.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
69.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify2.8s

Counts

164 → 164

Iterations

Iter	Nodes
done	5071
2	2643
1	658
0	236

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (cos th) (/ (sqrt (sqrt 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b	(/ (sqrt (sqrt 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))))

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

3516×	`times-frac`
2682×	`sqrt-prod`
1657×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
324×	`associate-/r*`
53×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
15×	`associate-/l*`
10×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log`

Counts

4 → 1554

Calls

4 calls:

12.0ms	(+ (* a1 a1) (* a2 a2))
128.0ms	(/ (cos th) (/ (sqrt (sqrt 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))))
38.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
40.0ms	(/ (sqrt (sqrt 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* a1 a1) (* a2 a2))
319.0ms	(/ (cos th) (/ (sqrt (sqrt 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))))
189.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
109.0ms	(/ (sqrt (sqrt 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))))

simplify4.0s

Counts

1566 → 1566

Iterations

Iter	Nodes
done	5000
1	4275
0	1444

prune6.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes539.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample5.9s

Algorithm

intervals

Results

1.9s	2543×	body	1280	valid
1.8s	8005×	body	80	valid
1.1s	2145×	body	640	valid
436.0ms	1061×	body	320	valid
175.0ms	522×	body	160	valid