Details

Time bar (total: 26.5s)

sample212.0ms

Algorithm
intervals
Results
88.0ms67×body1280valid
55.0ms46×body640valid
27.0ms112×body80valid
13.0ms17×body320valid
7.0ms14×body160valid

simplify994.0ms

Counts
1 → 1

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize55.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.0b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
0.2b
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
0.1b
(* (* J 2) (cos (/ K 2)))

rewrite686.0ms

Algorithm
rewrite-expression-head
Rules
98×add-cbrt-cube add-exp-log
49×prod-exp cbrt-unprod
26×pow1
24×cbrt-undiv div-exp
19×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
14×associate-*l*
12×times-frac
11×associate-*r*
10×pow-prod-down
7×swap-sqr
6×sqrt-prod
4×sqrt-div insert-posit16 div-inv add-log-exp
3×associate-*l/ *-commutative
2×flip3-+ flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 133
Calls
4 calls:
Slowest
357.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
167.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
139.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
21.0ms
(* (* J 2) (cos (/ K 2)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
239.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
154.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
133.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
56.0ms
(* (* J 2) (cos (/ K 2)))

simplify1.1s

Counts
145 → 145

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize58.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.0b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.0b
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
9.0b
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))

rewrite753.0ms

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
211.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
204.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
169.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
168.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series853.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
266.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
150.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
138.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify818.0ms

Counts
88 → 88

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

localize66.0ms

Local error

Found 4 expressions with local error:

17.6b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
17.6b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
17.6b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
13.2b
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))

rewrite424.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
Slowest
183.0ms
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
117.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
62.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
60.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
289.0ms
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
284.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
269.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
264.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify980.0ms

Counts
82 → 82

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.8b

localize101.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.0b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.0b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.0b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))

rewrite934.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*l/
1×associate-*r* *-commutative
Counts
4 → 75
Calls
4 calls:
Slowest
432.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
204.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
151.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
145.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series723.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
172.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
169.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
150.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.0s

Counts
87 → 87

prune2.0s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 7.8b

regimes549.0ms

Accuracy

-2% (8.7b remaining)

Error of 17.1b against oracle of 8.4b and baseline of 16.9b

bsearch390.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.4s1537×body1280valid
1.5s1204×body640valid
1.1s4338×body80valid
514.0ms644×body320valid
193.0ms281×body160valid