Details

sample164.0ms

Algorithm

intervals

Results

64.0ms	56×	body	1280	valid
29.0ms	37×	body	640	valid
28.0ms	140×	body	80	valid
17.0ms	15×	body	320	valid
3.0ms	8×	body	160	valid

simplify991.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize42.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
5.2b	(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
0.3b	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
0.1b	(* (cos (/ K 2)) (* -2 J))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-cbrt-cube` `add-exp-log`
26×	`pow1`
24×	`prod-exp` `cbrt-unprod`
19×	`add-sqr-sqrt`
18×	`associate-l`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`cbrt-undiv` `times-frac` `div-exp`
11×	`associate-r` `associate-*l/`
10×	`pow-prod-down`
9×	`swap-sqr`
8×	`associate-/r/`
6×	`flip3-+` `sqrt-prod` `flip-+`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`*-commutative`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*r/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

Slowest

218.0ms	(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
71.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
67.0ms	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
28.0ms	(* (cos (/ K 2)) (* -2 J))

series619.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

250.0ms	(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
156.0ms	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
146.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
66.0ms	(* (cos (/ K 2)) (* -2 J))

simplify1.1s

Counts: 137 → 137

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize46.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
5.2b	(* (* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
0.3b	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
0.1b	(* (+ J J) (cos (/ K 2)))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-cbrt-cube` `add-exp-log`
26×	`pow1`
24×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
21×	`-un-lft-identity` `associate-l*`
19×	`add-cube-cbrt`
15×	`associate-*l/`
13×	`associate-r`
12×	`cbrt-undiv` `times-frac` `div-exp`
10×	`pow-prod-down`
9×	`swap-sqr`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`distribute-rgt-out` `*-commutative` `sqrt-prod` `distribute-lft-out`
2×	`unswap-sqr`
1×	`pow2` `frac-times` `rem-sqrt-square` `distribute-lft1-in` `sqrt-pow1` `pow-plus` `pow1/2` `distribute-rgt1-in` `associate-*r/` `pow-sqr` `pow-prod-up`

Counts

4 → 133

Calls

4 calls:

Slowest

226.0ms	(* (* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
92.0ms	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
84.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
20.0ms	(* (+ J J) (cos (/ K 2)))

series623.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

267.0ms	(* (* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
157.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
136.0ms	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
62.0ms	(* (+ J J) (cos (/ K 2)))

simplify1.3s

Counts: 145 → 145

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize46.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
8.9b	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
5.3b	(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
5.3b	(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

Slowest

95.0ms	(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
86.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
84.0ms	(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
70.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

series810.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

259.0ms	(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
234.0ms	(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
160.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
157.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify882.0ms

Counts: 88 → 88

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize61.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
5.2b	(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.3b	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
0.3b	(cbrt (cos (/ K 2)))

rewrite554.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log`
59×	`add-cbrt-cube`
41×	`pow1`
37×	`prod-exp` `cbrt-unprod`
23×	`pow-prod-down`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`associate-l`
12×	`cbrt-undiv` `times-frac` `div-exp`
11×	`associate-*l/`
10×	`associate-r`
9×	`swap-sqr`
8×	`associate-/r/`
6×	`flip3-+` `sqrt-prod` `flip-+`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow1/3` `associate-*r/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

Slowest

388.0ms	(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
100.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
62.0ms	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
1.0ms	(cbrt (cos (/ K 2)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
144.0ms	(cbrt (cos (/ K 2)))
140.0ms	(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
140.0ms	(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))

simplify1.4s

Counts: 142 → 142

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

regimes534.0ms

Accuracy

7.2% (8.0b remaining)

Error of 16.3b against oracle of 8.3b and baseline of 16.9b

bsearch394.0ms

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.9s	1490×	body	1280	valid
1.8s	1255×	body	640	valid
1.2s	4309×	body	80	valid
574.0ms	672×	body	320	valid
138.0ms	276×	body	160	valid