Details

sample281.0ms

Algorithm

intervals

Results

92.0ms	267×	body	80	valid
86.0ms	71×	body	1280	valid
52.0ms	63×	body	640	valid
16.0ms	26×	body	320	valid
9.0ms	22×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

22.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
29.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms	(/ (cos th) (sqrt 2))
13.0ms	(/ (cos th) (sqrt 2))

series454.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
159.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
69.0ms	(/ (cos th) (sqrt 2))
85.0ms	(/ (cos th) (sqrt 2))

simplify2.9s

Counts

184 → 184

Iterations

Iter	Nodes
3	7244
2	1771
1	523
0	183

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 a2))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`associate-*l/`

Counts

4 → 136

Calls

4 calls:

21.0ms	(* (cos th) (* a2 a2))
39.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
26.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms	(/ (cos th) (sqrt 2))

series460.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (cos th) (* a2 a2))
173.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
138.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
75.0ms	(/ (cos th) (sqrt 2))

simplify4.7s

Counts

148 → 148

Iterations

Iter	Nodes
3	9508
2	1838
1	533
0	194

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 a2))
0.1b	(* (cos th) (* a1 a1))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
14×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
12×	`associate-/r*` `times-frac` `prod-exp` `sqrt-prod` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
4×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

20.0ms	(* (cos th) (* a2 a2))
15.0ms	(* (cos th) (* a1 a1))
41.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
19.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))

series457.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (cos th) (* a2 a2))
56.0ms	(* (cos th) (* a1 a1))
153.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
162.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))

simplify4.6s

Counts

112 → 112

Iterations

Iter	Nodes
3	9887
2	1647
1	430
0	156

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b	(/ (cos th) (sqrt (sqrt 2)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

1143×	`sqrt-prod`
1125×	`times-frac`
615×	`add-sqr-sqrt`
581×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
41×	`add-cbrt-cube` `add-exp-log`
35×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
13×	`cbrt-undiv` `div-exp` `unswap-sqr`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 738

Calls

4 calls:

39.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
51.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
25.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms	(/ (cos th) (sqrt (sqrt 2)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
143.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
83.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
121.0ms	(/ (cos th) (sqrt (sqrt 2)))

simplify2.3s

Counts

750 → 750

Iterations

Iter	Nodes
2	5808
1	1728
0	587

prune12.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes603.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.8s	2442×	body	1280	valid
2.5s	2085×	body	640	valid
1.5s	8032×	body	80	valid
658.0ms	1061×	body	320	valid
222.0ms	516×	body	160	valid