Details

sample182.0ms

Algorithm

intervals

Results

48.0ms	48×	body	1280	valid
47.0ms	36×	body	640	valid
25.0ms	133×	body	80	valid
15.0ms	24×	body	320	valid
6.0ms	16×	body	160	valid

simplify6.5s

Counts

1 → 1

Iterations

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

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize157.0ms

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))

rewrite1.2s

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` `insert-posit16` `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 → 100

Calls

4 calls:

20.0ms	(* (cos (/ K 2.0)) J)
98.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
735.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
335.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos (/ K 2.0)) J)
362.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
451.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
341.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify4.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1567
1	538
0	215

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize156.0ms

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))

rewrite262.0ms

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` `insert-posit16` `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 → 92

Calls

4 calls:

54.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
33.0ms	(* (cos (/ K 2.0)) J)
19.0ms	(* (cos (/ K 2.0)) J)
147.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
100.0ms	(* (cos (/ K 2.0)) J)
126.0ms	(* (cos (/ K 2.0)) J)
1.8s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

simplify4.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1602
1	453
0	186

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.8b

localize285.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
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)))
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)))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l` `sqrt-prod`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 83

Calls

4 calls:

19.0ms	(* (cos (/ K 2.0)) J)
443.0ms	(* (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)))
8.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
8.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series5.2s

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (cos (/ K 2.0)) J)
2.0s	(* (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)))
1.5s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.6s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify4.8s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1428
1	406
0	170

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.8b

localize333.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1`
19×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

79.0ms	(* (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))) (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))))
8.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
8.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
8.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series6.1s

Counts

4 → 12

Calls

4 calls:

1.7s	(* (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))) (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))))
1.5s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.5s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.5s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify4.6s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
3	2070
2	757
1	307
0	144

prune1.8s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.8b

regimes1.9s

Accuracy

-3.5% (4.3b remaining)

Error of 8.1b against oracle of 3.8b and baseline of 8.0b

bsearch414.0ms

Steps

Iters	Range		Point
9	2.7141933122050392e-247	9.683905674917091e-238	3.7183310343194604e-247
10	-3.710581581790982e-306	1.9760439910131958e-296	3.01385590437591e-302

simplify16.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.0s	1528×	body	1280	valid
1.1s	1353×	body	640	valid
844.0ms	4196×	body	80	valid
297.0ms	590×	body	320	valid
101.0ms	335×	body	160	valid