Details

sample293.0ms

Algorithm

intervals

Results

105.0ms	94×	body	1280	valid
92.0ms	86×	body	640	valid
42.0ms	264×	body	80	valid
25.0ms	50×	body	320	valid
7.0ms	22×	body	160	valid

simplify628.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

628.0ms

(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.4b

localize43.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (* J (exp l)) (/ J (exp l)))
0.0b	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
0.0b	(/ J (exp l))
0.0b	(* J (exp l))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`pow1` `add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `sub-neg` `div-inv` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `diff-log` `div-exp`

Counts

4 → 87

Calls

4 calls:

Slowest

60.0ms	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
21.0ms	(- (* J (exp l)) (/ J (exp l)))
17.0ms	(* J (exp l))
10.0ms	(/ J (exp l))

series265.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
85.0ms	(- (* J (exp l)) (/ J (exp l)))
35.0ms	(/ J (exp l))
25.0ms	(* J (exp l))

simplify4.0s

Counts

66 → 99

Calls

66 calls:

Slowest

781.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (- (* J (exp l)) (/ J (exp l))) (- (* J (exp l)) (/ J (exp l)))) (- (* J (exp l)) (/ J (exp l)))))
414.0ms	(/ (* (* J J) J) (* (* (exp l) (exp l)) (exp l)))
359.0ms	(* -1 (* (cos (* 1/2 K)) (* J (- (/ 1 (exp l)) (exp l)))))
288.0ms	(* (* (* J J) J) (* (* (exp l) (exp l)) (exp l)))
278.0ms	(* -1 (* J (- (/ 1 (exp l)) (exp l))))

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos (/ K 2)) (* 2 (* J l)))
0.0b	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
0.0b	(* 2 (* J l))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`insert-posit16`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

3 → 53

Calls

3 calls:

Slowest

67.0ms	(* (cos (/ K 2)) (* 2 (* J l)))
13.0ms	(* 2 (* J l))
9.0ms	(+ U (* (cos (/ K 2)) (* 2 (* J l))))

series257.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

143.0ms	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
83.0ms	(* (cos (/ K 2)) (* 2 (* J l)))
31.0ms	(* 2 (* J l))

simplify3.1s

Counts

30 → 62

Calls

30 calls:

Slowest

598.0ms	(* (* (* 2 2) 2) (* (* (* J l) (* J l)) (* J l)))
421.0ms	(* (* (* 2 2) 2) (* (* (* J J) J) (* (* l l) l)))
267.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* 2 2) 2) (* (* (* J J) J) (* (* l l) l))))
242.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* 2 (* J l)) (* 2 (* J l))) (* 2 (* J l))))
235.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* 2 2) 2) (* (* (* J l) (* J l)) (* J l))))

prune792.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

Slowest

8.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

242.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
160.0ms	(cbrt (cos (/ K 2)))
122.0ms	(cbrt (cos (/ K 2)))
122.0ms	(cbrt (cos (/ K 2)))

simplify2.0s

Counts

65 → 89

Calls

65 calls:

Slowest

413.0ms	(- 1 (+ (* 1/25920 (pow K 6)) (* 1/12 (pow K 2))))
196.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
180.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
145.0ms	(pow (pow (cos (* 1/2 K)) 2) 1/3)
144.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(* (cos (/ K 2)) (cos (/ K 2)))
0.1b	(* (cbrt (cos (/ K 2))) (* 2 (* J l)))
0.1b	(pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
18×	`add-exp-log`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
9×	`associate-l`
8×	`pow-prod-down` `prod-exp`
7×	`cbrt-unprod`
6×	`cbrt-prod` `pow-pow`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `swap-sqr`
2×	`pow2` `pow-plus` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow-to-exp` `sqr-cos` `unpow-prod-down` `unpow1/3` `pow1/3` `cos-mult` `unswap-sqr` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

Slowest

44.0ms	(* (cbrt (cos (/ K 2))) (* 2 (* J l)))
10.0ms	(* (cos (/ K 2)) (cos (/ K 2)))
6.0ms	(pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3)
1.0ms	(cbrt (cos (/ K 2)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

236.0ms	(pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3)
157.0ms	(* (cbrt (cos (/ K 2))) (* 2 (* J l)))
122.0ms	(cbrt (cos (/ K 2)))
24.0ms	(* (cos (/ K 2)) (cos (/ K 2)))

simplify3.1s

Counts

64 → 100

Calls

64 calls:

Slowest

381.0ms	(- 1 (+ (* 1/25920 (pow K 6)) (* 1/12 (pow K 2))))
184.0ms	(* 2 (* (pow (cos (* 1/2 K)) 1/3) (* J l)))
178.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
162.0ms	(pow (pow (cos (* 1/2 K)) 2) 1/3)
152.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes662.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample10.1s

Algorithm

intervals

Results

3.3s	2762×	body	1280	valid
3.0s	2656×	body	640	valid
2.0s	8383×	body	80	valid
939.0ms	1444×	body	320	valid
361.0ms	744×	body	160	valid