Details

sample156.0ms

Algorithm

intervals

Results

46.0ms	145×	body	80	valid
41.0ms	38×	body	1280	valid
32.0ms	39×	body	640	valid
13.0ms	24×	body	320	valid
5.0ms	10×	body	160	valid

simplify974.0ms

Counts: 1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize31.0ms

Local error

Found 4 expressions with local error:

8.0b	(* (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)))

rewrite132.0ms

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

71.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
28.0ms	(* J (* (cos (/ K 2)) 2))
16.0ms	(* (cos (/ K 2)) (* -2 J))
14.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

331.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
129.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
92.0ms	(* (cos (/ K 2)) (* -2 J))
64.0ms	(* J (* (cos (/ K 2)) 2))

simplify3.5s

Counts: 104 → 104

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize39.0ms

Local error

Found 4 expressions with local error:

8.1b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.1b	(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))))

rewrite159.0ms

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

114.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
41.0ms	(* (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)))))

series1.1s

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))))
314.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
246.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
211.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.8s

Counts: 101 → 101

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize53.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.4b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.4b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.1b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite6.0ms

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

406.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
366.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
326.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
212.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify872.0ms

Counts: 70 → 70

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize34.0ms

Local error

Found 4 expressions with local error:

8.0b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
1×	`associate-r` `*-commutative`

Counts

4 → 78

Calls

4 calls:

Slowest

221.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

373.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
171.0ms	(cbrt (cos (/ K 2)))
162.0ms	(cbrt (cos (/ K 2)))
147.0ms	(cbrt (cos (/ K 2)))

simplify3.3s

Counts: 90 → 90

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.3b

regimes576.0ms

Accuracy

-3.6% (4.0b remaining)

Error of 7.6b against oracle of 3.6b and baseline of 7.5b

bsearch166.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	1549×	body	1280	valid
2.0s	1239×	body	640	valid
975.0ms	4264×	body	80	valid
486.0ms	651×	body	320	valid
125.0ms	302×	body	160	valid