Details

sample189.0ms

Algorithm

intervals

Results

69.0ms	46×	body	1280	valid
40.0ms	40×	body	640	valid
36.0ms	141×	body	80	valid
14.0ms	19×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.0s

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize55.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

Slowest

40.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
15.0ms	(* J (* (cos (/ K 2)) 2))
14.0ms	(* (cos (/ K 2)) (* -2 J))
14.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

366.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
114.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
65.0ms	(* J (* (cos (/ K 2)) 2))
61.0ms	(* (cos (/ K 2)) (* -2 J))

simplify4.1s

Counts: 104 → 104

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize40.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.1b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

rewrite206.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 89

Calls

4 calls:

Slowest

160.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
42.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
1.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

321.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
314.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
286.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
251.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.6s

Counts: 101 → 101

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize83.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b	(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))

rewrite26.0ms

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:

Slowest

13.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
7.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series926.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

274.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
241.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
216.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
195.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify5.6s

Counts: 138 → 138

prune2.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.8b

localize117.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.8b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.8b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

1.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

354.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
342.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
331.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
227.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify944.0ms

Counts: 70 → 70

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.8b

regimes397.0ms

Accuracy

-18% (4.5b remaining)

Error of 8.4b against oracle of 3.8b and baseline of 7.7b

bsearch280.0ms

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.4s	1526×	body	1280	valid
1.4s	1206×	body	640	valid
1.2s	4301×	body	80	valid
573.0ms	641×	body	320	valid
163.0ms	330×	body	160	valid