Details

sample156.0ms

Algorithm

intervals

Results

46.0ms	53×	body	1280	valid
29.0ms	25×	body	320	valid
28.0ms	41×	body	640	valid
20.0ms	127×	body	80	valid
3.0ms	10×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize36.0ms

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)
7.4b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite358.0ms

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:

14.0ms	(* (cos (/ K 2.0)) J)
21.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
224.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
93.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series873.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cos (/ K 2.0)) J)
208.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
347.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
260.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1553
1	531
0	211

prune842.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize33.0ms

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)
7.4b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

rewrite84.0ms

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))
6.0ms	(* (cos (/ K 2.0)) J)
7.0ms	(* (cos (/ K 2.0)) J)
54.0ms	(* (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:

125.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
67.0ms	(* (cos (/ K 2.0)) J)
62.0ms	(* (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))

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1603
1	450
0	183

prune817.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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))
7.4b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
7.4b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

rewrite219.0ms

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:

127.0ms	(* (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)))
83.0ms	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
2.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
2.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series3.9s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (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)))
1.3s	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
803.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
809.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify3.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1427
1	409
0	162

prune966.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.9b

localize65.0ms

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	(* (hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0)) (* -2.0 (cos (/ K 2.0))))
0.2b	(/ (/ U J) (cos (/ K 2.0)))
7.4b	(* (* (hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0)) (* -2.0 (cos (/ K 2.0)))) J)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

0.0ms	(hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0))
15.0ms	(* (hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0)) (* -2.0 (cos (/ K 2.0))))
13.0ms	(/ (/ U J) (cos (/ K 2.0)))
71.0ms	(* (* (hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0)) (* -2.0 (cos (/ K 2.0)))) J)

series2.5s

Counts

4 → 12

Calls

4 calls:

689.0ms	(hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0))
771.0ms	(* (hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0)) (* -2.0 (cos (/ K 2.0))))
126.0ms	(/ (/ U J) (cos (/ K 2.0)))
865.0ms	(* (* (hypot (pow (/ (/ (/ U J) (cos (/ K 2.0))) 2.0) (/ 2.0 2)) (sqrt 1.0)) (* -2.0 (cos (/ K 2.0)))) J)

simplify2.1s

Counts

137 → 137

Iterations

Iter	Nodes
done	5011
2	1954
1	644
0	276

prune1.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.9b

regimes930.0ms

Accuracy

-3.7% (4.2b remaining)

Error of 8.3b against oracle of 4.1b and baseline of 8.1b

bsearch125.0ms

Steps

Iters	Range		Point
6	2.9613139026136572e+256	2.589187708518178e+257	2.3500796131724043e+257

simplify36.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	1263×	body	640	valid
1.1s	4322×	body	80	valid
1.0s	1451×	body	1280	valid
211.0ms	622×	body	320	valid
130.0ms	342×	body	160	valid