Details

Time bar (total: 1.0m)

sample186.0ms

Algorithm
intervals
Results
68.0ms42×body1280valid
44.0ms41×body640valid
34.0ms142×body80valid
13.0ms18×body320valid
7.0ms13×body160valid

simplify254.0ms

Calls
1 calls:
Slowest
253.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize25.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(* (cos (/ K 2)) (* -2 J))
0.1b
(/ U (* J (* (cos (/ K 2)) 2)))

rewrite164.0ms

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
Calls
4 calls:
Slowest
70.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
36.0ms
(* J (* (cos (/ K 2)) 2))
29.0ms
(* (cos (/ K 2)) (* -2 J))
27.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series609.0ms

Calls
4 calls:
Slowest
360.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
112.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
72.0ms
(* J (* (cos (/ K 2)) 2))
64.0ms
(* (cos (/ K 2)) (* -2 J))

simplify6.9s

Calls
55 calls:
Slowest
823.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
483.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
466.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
325.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))
325.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.7b

localize36.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
0.1b
(/ U (* J (* (cos (/ K 2)) 2)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
41×add-cbrt-cube add-exp-log
32×pow1
22×prod-exp cbrt-unprod
19×pow-prod-down
12×associate-*l*
10×add-sqr-sqrt *-un-lft-identity 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 sqrt-prod associate-/l*
1×clear-num associate-/r* frac-2neg div-inv
Calls
4 calls:
Slowest
147.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
68.0ms
(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
28.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
15.0ms
(* J (* (cos (/ K 2)) 2))

series606.0ms

Calls
4 calls:
Slowest
353.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
115.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
73.0ms
(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
65.0ms
(* J (* (cos (/ K 2)) 2))

simplify8.9s

Calls
65 calls:
Slowest
473.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* (sqrt (cos (/ K 2))) (* -2 J)) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
462.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
440.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
416.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
409.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize45.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))
0.1b
(* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))

rewrite708.0ms

Algorithm
rewrite-expression-head
Rules
52×pow1 add-cbrt-cube add-exp-log
34×pow-prod-down prod-exp cbrt-unprod
24×associate-*l*
18×sqrt-prod
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u associate-*r* *-commutative insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
445.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
158.0ms
(* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))
74.0ms
(* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))
30.0ms
(* J (* (cos (/ K 2)) 2))

series675.0ms

Calls
4 calls:
Slowest
354.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
151.0ms
(* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))
85.0ms
(* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))
83.0ms
(* J (* (cos (/ K 2)) 2))

simplify13.5s

Calls
77 calls:
Slowest
819.0ms
(* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
742.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* -2 -2) -2) (* (* J J) J))))))
618.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (cos (/ K 2))) (* -2 J)) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (sqrt (cos (/ K 2))) (* -2 J))))))
551.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (sqrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))))
533.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J))))))

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize63.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))))
0.3b
(* (cos (* K 1/2)) (cos (* K 1/2)))
0.1b
(* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2))))
0.1b
(* J (* (cos (/ K 2)) 2))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
39×pow1
36×prod-exp
30×add-cbrt-cube
17×cbrt-unprod
14×add-sqr-sqrt
13×pow-prod-down
12×associate-*l*
11×*-un-lft-identity add-cube-cbrt
6×associate-*r* pow-prod-up
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×sqr-cos swap-sqr pow-exp
2×pow2 pow-plus pow-sqr cos-mult unswap-sqr
1×distribute-rgt-in pow-to-exp distribute-lft-in cube-unmult associate-*r/
Calls
4 calls:
Slowest
1.1s
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))))
72.0ms
(* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2))))
37.0ms
(* (cos (* K 1/2)) (cos (* K 1/2)))
23.0ms
(* J (* (cos (/ K 2)) 2))

series480.0ms

Calls
4 calls:
Slowest
340.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))))
69.0ms
(* J (* (cos (/ K 2)) 2))
42.0ms
(* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2))))
29.0ms
(* (cos (* K 1/2)) (cos (* K 1/2)))

simplify11.8s

Calls
82 calls:
Slowest
886.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))))))
859.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* -2 -2) -2) (* (* (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)) (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))) (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))))))
780.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* -2 -2) -2) (* (* (* J J) J) (* (* (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4) (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)) (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))))))
713.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (sqrt (cos (/ K 2)))) (sqrt (sqrt (cos (/ K 2))))) (sqrt (sqrt (cos (/ K 2))))) (* (* (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4))))))
545.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))))

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

regimes391.0ms

Accuracy

0% (3.6b remaining)

Error of 7.2b against oracle of 3.5b and baseline of 7.2b

bsearch5.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.0s1479×body1280valid
1.8s1292×body640valid
1.5s4304×body80valid
509.0ms602×body320valid
178.0ms324×body160valid