Details

sample130.0ms

Algorithm

intervals

Results

48.0ms	40×	body	640	valid
32.0ms	49×	body	1280	valid
17.0ms	140×	body	80	valid
6.0ms	13×	body	320	valid
3.0ms	14×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2639
6	722
5	279
4	166
3	112
2	69
1	34
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
0.2b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
7.6b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
10.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`pow1`
16×	`*-un-lft-identity`
15×	`add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`associate-l` `prod-exp`
8×	`unpow-prod-down` `sqrt-prod`
7×	`pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `associate-r` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

8.0ms	(* (cos (/ K 2.0)) J)
18.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
279.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
117.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series801.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos (/ K 2.0)) J)
176.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
351.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
210.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify1.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1553
1	531
0	211

prune817.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
0.1b	(* (cos (/ K 2.0)) J)
0.1b	(* (cos (/ K 2.0)) J)
7.6b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`associate-l`
8×	`pow-prod-down`
7×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
2×	`unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 88

Calls

4 calls:

15.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
9.0ms	(* (cos (/ K 2.0)) J)
6.0ms	(* (cos (/ K 2.0)) J)
72.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
77.0ms	(* (cos (/ K 2.0)) J)
60.0ms	(* (cos (/ K 2.0)) J)
1.0s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1603
1	450
0	183

prune613.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
0.2b	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
7.7b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
7.7b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
27×	`add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-l` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 85

Calls

4 calls:

119.0ms	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
51.0ms	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
1.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
1.1s	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
784.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
762.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify3.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1427
1	409
0	162

prune903.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
7.6b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
1×	`associate-r` `*-commutative`

Counts

4 → 71

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
426.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (cos (/ K 2.0)))
236.0ms	(cbrt (cos (/ K 2.0)))
204.0ms	(cbrt (cos (/ K 2.0)))
1.0s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))

simplify2.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1539
1	413
0	161

prune593.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

regimes800.0ms

Accuracy

-0.9% (4.3b remaining)

Error of 8.2b against oracle of 3.9b and baseline of 8.2b

bsearch129.0ms

Steps

Iters	Range		Point
9	-8.615939914099502e+266	-2.1784825593516065e+257	-7.162239869679763e+262

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.2s	1487×	body	1280	valid
1.2s	1300×	body	640	valid
698.0ms	4239×	body	80	valid
686.0ms	647×	body	320	valid
134.0ms	330×	body	160	valid