Details

sample210.0ms

Algorithm

intervals

Results

78.0ms	40×	body	1280	valid
48.0ms	42×	body	640	valid
43.0ms	146×	body	80	valid
11.0ms	13×	body	320	valid
9.0ms	15×	body	160	valid

simplify300.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

300.0ms

(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize27.0ms

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

rewrite119.0ms

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)))
24.0ms	(* (cos (/ K 2)) (* -2 J))
14.0ms	(* J (* (cos (/ K 2)) 2))
12.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

358.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
133.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
84.0ms	(* (cos (/ K 2)) (* -2 J))
75.0ms	(* J (* (cos (/ K 2)) 2))

simplify13.0s

Counts

105 → 104

Calls

105 calls:

Slowest

621.0ms	(* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2)))
550.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
536.0ms	(* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J)))
465.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
450.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

localize35.0ms

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	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

Slowest

73.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
13.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
3.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

670.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
235.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
230.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
111.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

simplify10.9s

Counts

102 → 97

Calls

102 calls:

Slowest

403.0ms	(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
336.0ms	(- (log U) (+ (log J) (+ (log (cos (/ K 2))) (log 2))))
328.0ms	(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
314.0ms	(- (log U) (+ (log J) (log (* (cos (/ K 2)) 2))))
309.0ms	(/ (* (* U U) U) (* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize97.0ms

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
27×	`add-cbrt-cube`
25×	`prod-exp`
17×	`pow1`
15×	`add-sqr-sqrt`
13×	`cbrt-unprod`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l` `sqrt-prod`
8×	`associate-r`
7×	`pow-prod-down`
6×	`div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `times-frac` `1-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`
1×	`associate-*r/` `un-div-inv` `div-inv` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

Slowest

76.0ms	(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
58.0ms	(* (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))

series884.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

300.0ms	(* (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))
248.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
213.0ms	(sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))
123.0ms	(* U (/ 1 (* J (* (cos (/ K 2)) 2))))

simplify27.2s

Counts

110 → 110

Calls

110 calls:

Slowest

693.0ms	(* (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))
548.0ms	(* (* (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))) (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))))
526.0ms	(* (cbrt (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))) (cbrt (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))))
503.0ms	(cbrt (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))))
491.0ms	(* (cbrt U) (/ 1 (* J (* (cos (/ K 2)) 2))))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.5b

localize120.0ms

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 (* (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))))
0.6b	(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
0.6b	(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv`

Counts

4 → 70

Calls

4 calls:

Slowest

19.0ms	(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
14.0ms	(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (* (* U (* (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

352.0ms	(sqrt (hypot 1 (* (* U (* (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))))
239.0ms	(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
210.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
202.0ms	(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))

simplify8.6s

Counts

98 → 82

Calls

98 calls:

Slowest

423.0ms	(* (cbrt -1/2) (exp (* 1/3 (+ (log (/ 1 (cos (* 1/2 K)))) (log (/ -1 J))))))
404.0ms	(* (cbrt 1/2) (exp (* 1/3 (+ (log (/ 1 (cos (* 1/2 K)))) (log (/ 1 J))))))
388.0ms	(* (cbrt -1/2) (exp (* 1/3 (+ (log (/ 1 (cos (* 1/2 K)))) (log (/ -1 J))))))
369.0ms	(* (cbrt 1/2) (exp (* 1/3 (+ (log (/ 1 (cos (* 1/2 K)))) (log (/ 1 J))))))
337.0ms	(+ (* (cbrt 1/2) (pow (/ 1 J) 1/3)) (* 1/24 (* (* (cbrt 1/2) (pow K 2)) (pow (/ 1 J) 1/3))))

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.5b

regimes401.0ms

Accuracy

0% (3.7b remaining)

Error of 7.8b against oracle of 4.0b and baseline of 7.8b

bsearch3.0ms

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.6s	1515×	body	1280	valid
1.6s	4296×	body	80	valid
1.3s	1237×	body	640	valid
402.0ms	602×	body	320	valid
198.0ms	352×	body	160	valid