Details

sample114.0ms

Algorithm

intervals

Results

46.0ms	57×	body	1280	valid
19.0ms	42×	body	640	valid
15.0ms	132×	body	80	valid
6.0ms	16×	body	320	valid
2.0ms	9×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3226
5	495
4	209
3	135
2	72
1	34
0	17

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
0.3b	(pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)
6.7b	(* (* (* (sqrt (+ (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0) 1.0)) -2.0) (cos (/ K 2.0))) J)
11.3b	(sqrt (+ (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0) 1.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
38×	`add-exp-log`
35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`add-cbrt-cube`
18×	`unpow-prod-down`
15×	`pow1`
13×	`associate-/l*`
12×	`div-exp`
10×	`prod-exp`
8×	`cbrt-unprod`
6×	`cbrt-undiv` `pow-prod-down` `associate-*l/`
5×	`pow-exp` `div-inv`
4×	`expm1-log1p-u` `sqrt-div` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `hypot-def`
2×	`flip3-+` `flip-+` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `-commutative` `distribute-lft-out` `associate-/l/`

Counts

4 → 131

Calls

4 calls:

11.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
13.0ms	(pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)
922.0ms	(* (* (* (sqrt (+ (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0) 1.0)) -2.0) (cos (/ K 2.0))) J)
136.0ms	(sqrt (+ (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0) 1.0))

series816.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
173.0ms	(pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)
286.0ms	(* (* (* (sqrt (+ (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0) 1.0)) -2.0) (cos (/ K 2.0))) J)
244.0ms	(sqrt (+ (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0) 1.0))

simplify1.7s

Counts

143 → 143

Iterations

Iter	Nodes
done	5002
2	3751
1	857
0	299

prune939.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))
0.1b	(* (* (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)) -2.0) (cos (/ K 2.0)))
0.1b	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
6.7b	(* (* (* (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)) -2.0) (cos (/ K 2.0))) J)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
13×	`associate-/l*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
6×	`cbrt-undiv` `div-exp` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`associate-l` `*-commutative`
1×	`hypot-udef` `clear-num` `associate-/r*` `frac-2neg` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

0.0ms	(hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))
20.0ms	(* (* (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)) -2.0) (cos (/ K 2.0)))
11.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
70.0ms	(* (* (* (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)) -2.0) (cos (/ K 2.0))) J)

series2.3s

Counts

4 → 12

Calls

4 calls:

668.0ms	(hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))
657.0ms	(* (* (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)) -2.0) (cos (/ K 2.0)))
126.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
876.0ms	(* (* (* (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)) -2.0) (cos (/ K 2.0))) J)

simplify1.9s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	2949
1	595
0	244

prune900.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (pow (/ (/ U J) (* (cos (/ K 2.0)) 2.0)) (/ 2.0 2)) (sqrt 1.0))
0.1b	(/ (/ U J) (* (cos (/ K 2.0)) 2.0))
0.1b	(* (* -2.0 (cos (/ K 2.0))) J)
6.7b	(* (hypot (pow (/ (/ U J) (* (cos (/ K 2.0)) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* -2.0 (cos (/ K 2.0))) J))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
13×	`associate-/l*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`*-commutative`
1×	`hypot-udef` `clear-num` `associate-/r*` `frac-2neg` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

0.0ms	(hypot (pow (/ (/ U J) (* (cos (/ K 2.0)) 2.0)) (/ 2.0 2)) (sqrt 1.0))
22.0ms	(/ (/ U J) (* (cos (/ K 2.0)) 2.0))
19.0ms	(* (* -2.0 (cos (/ K 2.0))) J)
65.0ms	(* (hypot (pow (/ (/ U J) (* (cos (/ K 2.0)) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* -2.0 (cos (/ K 2.0))) J))

series1.6s

Counts

4 → 12

Calls

4 calls:

603.0ms	(hypot (pow (/ (/ U J) (* (cos (/ K 2.0)) 2.0)) (/ 2.0 2)) (sqrt 1.0))
131.0ms	(/ (/ U J) (* (cos (/ K 2.0)) 2.0))
67.0ms	(* (* -2.0 (cos (/ K 2.0))) J)
778.0ms	(* (hypot (pow (/ (/ U J) (* (cos (/ K 2.0)) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* -2.0 (cos (/ K 2.0))) J))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	2579
1	589
0	241

prune944.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))
0.1b	(* (* -2.0 (cos (/ K 2.0))) (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)))
0.1b	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
6.7b	(* (* (* -2.0 (cos (/ K 2.0))) (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))) J)

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
13×	`associate-/l*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
6×	`cbrt-undiv` `div-exp` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`associate-l` `*-commutative`
1×	`hypot-udef` `clear-num` `associate-/r*` `frac-2neg` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

0.0ms	(hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))
31.0ms	(* (* -2.0 (cos (/ K 2.0))) (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)))
21.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
90.0ms	(* (* (* -2.0 (cos (/ K 2.0))) (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))) J)

series2.6s

Counts

4 → 12

Calls

4 calls:

631.0ms	(hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))
714.0ms	(* (* -2.0 (cos (/ K 2.0))) (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0)))
147.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
1.1s	(* (* (* -2.0 (cos (/ K 2.0))) (hypot (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) (/ 2.0 2)) (sqrt 1.0))) J)

simplify1.7s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	3474
1	701
0	272

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.5b

regimes801.0ms

Accuracy

-21.8% (5.5b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 8.3b

bsearch408.0ms

Steps

Iters	Range		Point
10	5.589580785508872e-177	4.5529622625386965e-164	6.9954698652813445e-177
10	-2.631585147976807e-302	9.07677113687735e-304	-5.6753724859014906e-306

simplify9.0ms

Iterations

Iter	Nodes
done	42
1	42
0	31

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.6s	1503×	body	1280	valid
1.4s	1300×	body	640	valid
778.0ms	4264×	body	80	valid
239.0ms	632×	body	320	valid
198.0ms	306×	body	160	valid