Details

Time bar (total: 56.4s)

sample197.0ms

Algorithm
intervals
Results
55.0ms42×body1280valid
46.0ms45×body640valid
46.0ms134×body80valid
21.0ms28×body320valid
3.0ms7×body160valid

simplify271.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
271.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize41.0ms

Local error

Found 4 expressions with local error:

11.5b
(* (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)))

rewrite95.0ms

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
38.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
22.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
19.0ms
(* (cos (/ K 2)) (* -2 J))
14.0ms
(* J (* (cos (/ K 2)) 2))

series615.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
345.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
108.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
83.0ms
(* (cos (/ K 2)) (* -2 J))
80.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.8s

Counts
55 → 104
Calls
55 calls:
Slowest
520.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
514.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
448.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
363.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))
360.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

localize82.0ms

Local error

Found 4 expressions with local error:

11.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
11.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
11.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.6b
(cbrt (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J))))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1 add-cbrt-cube add-exp-log
18×pow-prod-down prod-exp cbrt-unprod
9×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* *-commutative
1×cbrt-prod pow1/3
Counts
4 → 84
Calls
4 calls:
Slowest
66.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
45.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
41.0ms
(cbrt (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J))))
38.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
497.0ms
(cbrt (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J))))
340.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
338.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
334.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))

simplify7.3s

Counts
49 → 96
Calls
49 calls:
Slowest
375.0ms
(* (* (* (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))))
345.0ms
(* (cbrt -2) (exp (* 1/3 (- (log 1/2) (log (/ 1 U))))))
338.0ms
(* (* (* (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))))
333.0ms
(* (* (* (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))))
287.0ms
(* (* (* (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)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J))))

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.6b

localize43.0ms

Local error

Found 4 expressions with local error:

9.1b
(* (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)))

rewrite196.0ms

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
Counts
4 → 101
Calls
4 calls:
Slowest
116.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
47.0ms
(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
18.0ms
(* J (* (cos (/ K 2)) 2))
13.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
357.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
126.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
66.0ms
(* J (* (cos (/ K 2)) 2))
64.0ms
(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))

simplify9.5s

Counts
65 → 113
Calls
65 calls:
Slowest
727.0ms
(- (log U) (+ (log J) (+ (log (cos (/ K 2))) (log 2))))
542.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
463.0ms
(* (* (* (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)))))
410.0ms
(* (* (* (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)))))
396.0ms
(* (* (* (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))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.6b

localize44.0ms

Local error

Found 4 expressions with local error:

9.1b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
0.2b
(cbrt (sqrt (cos (/ K 2))))
0.2b
(cbrt (sqrt (cos (/ K 2))))
0.2b
(cbrt (sqrt (cos (/ K 2))))

rewrite424.0ms

Algorithm
rewrite-expression-head
Rules
46×pow1 add-exp-log
33×pow-prod-down prod-exp cbrt-unprod
32×add-cbrt-cube
18×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* *-commutative
Counts
4 → 93
Calls
4 calls:
Slowest
419.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
1.0ms
(cbrt (sqrt (cos (/ K 2))))
1.0ms
(cbrt (sqrt (cos (/ K 2))))
1.0ms
(cbrt (sqrt (cos (/ K 2))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
176.0ms
(cbrt (sqrt (cos (/ K 2))))
153.0ms
(cbrt (sqrt (cos (/ K 2))))
135.0ms
(cbrt (sqrt (cos (/ K 2))))

simplify14.5s

Counts
60 → 105
Calls
60 calls:
Slowest
967.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (* (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))))
832.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))) (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))))
646.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (sqrt (cos (/ K 2))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* -2 -2) -2) (* (* J J) J))))))
588.0ms
(* (* (* (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)))) (* (* (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (cbrt (sqrt (cos (/ K 2)))) (* (sqrt (cos (/ K 2))) (* -2 J))))))
582.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2))))) (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (cbrt (sqrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (sqrt (cos (/ K 2))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J))))))

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.6b

regimes496.0ms

Accuracy

-36.8% (5.2b remaining)

Error of 9.3b against oracle of 4.2b and baseline of 7.9b

bsearch440.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.5s1497×body1280valid
1.6s1263×body640valid
1.1s4357×body80valid
475.0ms591×body320valid
169.0ms295×body160valid