Details

sample200.0ms

Algorithm

intervals

Results

73.0ms	59×	body	1280	valid
58.0ms	41×	body	640	valid
27.0ms	126×	body	80	valid
11.0ms	18×	body	320	valid
6.0ms	12×	body	160	valid

simplify1.6s

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize69.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (* (cos (/ K 2)) J))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(* (cos (/ K 2)) J)
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

Slowest

25.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (* (cos (/ K 2)) J))
22.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
14.0ms	(* J (* (cos (/ K 2)) 2))
13.0ms	(* (cos (/ K 2)) J)

series616.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

335.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (* (cos (/ K 2)) J))
132.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
81.0ms	(* J (* (cos (/ K 2)) 2))
68.0ms	(* (cos (/ K 2)) J)

simplify3.5s

Counts: 105 → 105

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize69.0ms

Local error

Found 4 expressions with local error:

8.7b	(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (cos (/ K 2))) J)
0.3b	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (cos (/ K 2)))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite186.0ms

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` `add-cube-cbrt`
7×	`associate-r`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

Slowest

94.0ms	(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (cos (/ K 2))) J)
31.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (cos (/ K 2)))
30.0ms	(* J (* (cos (/ K 2)) 2))
26.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series883.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

381.0ms	(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (cos (/ K 2))) J)
295.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (cos (/ K 2)))
122.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
84.0ms	(* J (* (cos (/ K 2)) 2))

simplify3.6s

Counts: 104 → 104

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize43.0ms

Local error

Found 4 expressions with local error:

8.7b	(* (* (* -2 (cos (/ K 2))) (hypot 1 (/ (/ (/ U J) (cos (/ K 2))) 2))) J)
0.2b	(/ (/ (/ U J) (cos (/ K 2))) 2)
0.1b	(/ (/ U J) (cos (/ K 2)))
0.1b	(* (* -2 (cos (/ K 2))) (hypot 1 (/ (/ (/ U J) (cos (/ K 2))) 2)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac`
232×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
56×	`associate-/l*`
32×	`add-cbrt-cube` `add-exp-log`
22×	`div-inv`
18×	`pow1`
9×	`cbrt-undiv` `div-exp` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 313

Calls

4 calls:

Slowest

78.0ms	(* (* (* -2 (cos (/ K 2))) (hypot 1 (/ (/ (/ U J) (cos (/ K 2))) 2))) J)
32.0ms	(* (* -2 (cos (/ K 2))) (hypot 1 (/ (/ (/ U J) (cos (/ K 2))) 2)))
24.0ms	(/ (/ (/ U J) (cos (/ K 2))) 2)
15.0ms	(/ (/ U J) (cos (/ K 2)))

series966.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

385.0ms	(* (* (* -2 (cos (/ K 2))) (hypot 1 (/ (/ (/ U J) (cos (/ K 2))) 2))) J)
345.0ms	(* (* -2 (cos (/ K 2))) (hypot 1 (/ (/ (/ U J) (cos (/ K 2))) 2)))
139.0ms	(/ (/ (/ U J) (cos (/ K 2))) 2)
98.0ms	(/ (/ U J) (cos (/ K 2)))

simplify673.0ms

Counts: 325 → 325

prune5.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize85.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))
0.4b	(cbrt (cos (/ K 2)))
0.4b	(cbrt (cos (/ K 2)))
0.4b	(cbrt (cos (/ K 2)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

Slowest

141.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))

series803.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

344.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) -2) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))
166.0ms	(cbrt (cos (/ K 2)))
154.0ms	(cbrt (cos (/ K 2)))
139.0ms	(cbrt (cos (/ K 2)))

simplify3.9s

Counts: 97 → 97

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.3b

regimes559.0ms

Accuracy

-5.7% (4.0b remaining)

Error of 8.0b against oracle of 4.0b and baseline of 7.7b

bsearch218.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	1553×	body	1280	valid
1.2s	1260×	body	640	valid
1.1s	4281×	body	80	valid
368.0ms	613×	body	320	valid
182.0ms	294×	body	160	valid