Details

sample171.0ms

Algorithm

intervals

Results

79.0ms	67×	body	1280	valid
35.0ms	46×	body	640	valid
21.0ms	112×	body	80	valid
9.0ms	17×	body	320	valid
5.0ms	14×	body	160	valid

simplify963.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize52.0ms

Local error

Found 4 expressions with local error:

9.0b	(* (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)))

rewrite127.0ms

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

67.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
23.0ms	(* J (* (cos (/ K 2)) 2))
21.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
14.0ms	(* (cos (/ K 2)) (* -2 J))

series586.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

331.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
106.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
77.0ms	(* (cos (/ K 2)) (* -2 J))
71.0ms	(* J (* (cos (/ K 2)) 2))

simplify3.1s

Counts: 104 → 104

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

localize74.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.0b	(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)))
0.2b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

rewrite185.0ms

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

141.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
37.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
3.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

330.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
326.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
265.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
219.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.7s

Counts: 101 → 101

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.0b

localize108.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.3b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.3b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.0b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite7.0ms

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

2.0ms	(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

381.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
346.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
307.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
258.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify665.0ms

Counts: 70 → 70

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.0b

localize78.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.0b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.0b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
9.0b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

Slowest

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

series912.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

234.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
234.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
230.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
214.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify5.2s

Counts: 76 → 76

prune1.3s

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 4.0b

regimes511.0ms

Accuracy

0% (3.9b remaining)

Error of 7.9b against oracle of 4.0b and baseline of 7.9b

bsearch5.0ms

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.1s	1537×	body	1280	valid
1.6s	4338×	body	80	valid
1.2s	1204×	body	640	valid
847.0ms	644×	body	320	valid
191.0ms	281×	body	160	valid