Details

Time bar (total: 1.0m)

sample135.0ms

Algorithm
intervals
Results
46.0ms45×body640valid
30.0ms34×body1280valid
29.0ms153×body80valid
8.0ms15×body320valid
3.0ms9×body160valid

simplify284.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
284.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize40.0ms

Local error

Found 4 expressions with local error:

9.9b
(* (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)))

rewrite124.0ms

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
(/ U (* J (* (cos (/ K 2)) 2)))
17.0ms
(* (cos (/ K 2)) (* -2 J))
15.0ms
(* J (* (cos (/ K 2)) 2))

series601.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
118.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
80.0ms
(* (cos (/ K 2)) (* -2 J))
71.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.8s

Counts
55 → 104
Calls
55 calls:
Slowest
496.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
453.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
441.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
370.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))
354.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize59.0ms

Local error

Found 4 expressions with local error:

9.9b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log
23×add-cbrt-cube
22×pow-prod-down prod-exp cbrt-unprod
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* *-commutative
Counts
4 → 78
Calls
4 calls:
Slowest
189.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
166.0ms
(cbrt (cos (/ K 2)))
135.0ms
(cbrt (cos (/ K 2)))
131.0ms
(cbrt (cos (/ K 2)))

simplify10.2s

Counts
45 → 90
Calls
45 calls:
Slowest
866.0ms
(* (* (* (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))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
805.0ms
(* (* (* (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 (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
636.0ms
(* (* (* (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 (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
464.0ms
(+ (log (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (+ (+ (log (cbrt (cos (/ K 2)))) (log (cbrt (cos (/ K 2))))) (+ (log (cbrt (cos (/ K 2)))) (+ (log -2) (log J)))))
449.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize57.0ms

Local error

Found 4 expressions with local error:

9.9b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.3b
(cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log
23×add-cbrt-cube
22×pow-prod-down prod-exp cbrt-unprod
7×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* pow3 *-commutative rem-cbrt-cube
Counts
4 → 77
Calls
4 calls:
Slowest
263.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))
22.0ms
(cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series802.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
300.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))
187.0ms
(cbrt (cos (/ K 2)))
176.0ms
(cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))
139.0ms
(cbrt (cos (/ K 2)))

simplify10.0s

Counts
44 → 89
Calls
44 calls:
Slowest
724.0ms
(* (* (* (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 (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2))))))) (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2))))))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
565.0ms
(* (* (* (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 (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
472.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))
464.0ms
(* (* (* (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)) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2))))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
463.0ms
(+ (log (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (+ (log (* (cbrt (cos (/ K 2))) (cbrt (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2))))))) (+ (log (cbrt (cos (/ K 2)))) (+ (log -2) (log J)))))

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize89.0ms

Local error

Found 4 expressions with local error:

9.9b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.3b
(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite455.0ms

Algorithm
rewrite-expression-head
Rules
51×pow1 add-exp-log
37×pow-prod-down prod-exp cbrt-unprod
33×add-cbrt-cube
7×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* *-commutative
Counts
4 → 85
Calls
4 calls:
Slowest
442.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
8.0ms
(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))
2.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
322.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
165.0ms
(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))
146.0ms
(cbrt (cos (/ K 2)))
131.0ms
(cbrt (cos (/ K 2)))

simplify16.3s

Counts
52 → 97
Calls
52 calls:
Slowest
1.4s
(* (* (* (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 (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
1.1s
(* (* (* (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 (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (cos (/ K 2)) (* (* (* -2 J) (* -2 J)) (* -2 J)))))
1.1s
(* (* (* (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 (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
1.1s
(* (* (* (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 (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (cos (/ K 2))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
914.0ms
(* (* (* (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 (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (cos (/ K 2)) (* (* (* -2 -2) -2) (* (* J J) J)))))

prune1.7s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.6b

regimes522.0ms

Accuracy

-15.4% (4.6b remaining)

Error of 8.6b against oracle of 3.9b and baseline of 8.0b

bsearch176.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.8s1439×body1280valid
1.4s1230×body640valid
1.2s4415×body80valid
442.0ms585×body320valid
213.0ms333×body160valid