Details

Time bar (total: 4.1m)

sample193.0ms

Algorithm
intervals
Results
66.0ms48×body1280valid
56.0ms36×body640valid
38.0ms147×body80valid
11.0ms15×body320valid
5.0ms10×body160valid

simplify310.0ms

Calls
1 calls:
Slowest
309.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.4b

localize48.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (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)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
127×associate-*r*
119×add-sqr-sqrt
66×times-frac
61×*-un-lft-identity add-cube-cbrt
45×associate-*l*
34×unswap-sqr
32×add-cbrt-cube add-exp-log
23×pow1
22×associate-/r*
15×prod-exp *-commutative cbrt-unprod
12×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
1×clear-num frac-2neg div-inv
Calls
4 calls:
Slowest
116.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
62.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
54.0ms
(* J (* (cos (/ K 2)) 2))
27.0ms
(* (cos (/ K 2)) (* -2 J))

series636.0ms

Calls
4 calls:
Slowest
349.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
130.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
80.0ms
(* J (* (cos (/ K 2)) 2))
76.0ms
(* (cos (/ K 2)) (* -2 J))

simplify14.6s

Calls
250 calls:
Slowest
876.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
520.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
515.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
399.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
351.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))

prune3.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize48.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.1b
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
127×add-sqr-sqrt
113×associate-*r*
70×unswap-sqr
34×sqrt-prod
30×associate-*l*
29×pow1
27×add-cbrt-cube add-exp-log
23×*-un-lft-identity add-cube-cbrt
16×pow-prod-down prod-exp cbrt-unprod
7×*-commutative
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
259.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
87.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Calls
4 calls:
Slowest
409.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
311.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
230.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
227.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify16.2s

Calls
148 calls:
Slowest
480.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))))
479.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))))
412.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))))
400.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J)))))
359.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))

prune2.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.8b

localize38.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
3.6b
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J))))

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
397×add-sqr-sqrt
284×unswap-sqr
201×sqrt-prod
91×associate-*r*
47×associate-*l*
39×pow1
36×add-cbrt-cube add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
22×*-un-lft-identity add-cube-cbrt
5×*-commutative
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
413.0ms
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Calls
4 calls:
Slowest
353.0ms
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J))))
307.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
283.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
282.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify51.6s

Calls
257 calls:
Slowest
1.1s
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))) (* (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))))
743.0ms
(* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))) (* (sqrt (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (sqrt (cos (/ K 2))) (sqrt (* -2 J)))))
710.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))) (* (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))))
661.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))) (* (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J))) (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))) (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))))
626.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))) (* (* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J)))))

prune3.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.8b

localize61.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.8b
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J)))))) (cbrt J))
0.6b
(cbrt J)

rewrite4.8s

Algorithm
rewrite-expression-head
Rules
963×add-sqr-sqrt
748×unswap-sqr
240×associate-*r*
176×associate-*l*
165×cbrt-prod
158×sqrt-prod
83×add-cbrt-cube
78×cbrt-unprod
38×swap-sqr
33×pow1
31×add-exp-log
28×*-un-lft-identity add-cube-cbrt
22×*-commutative
21×pow-prod-down prod-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Calls
4 calls:
Slowest
4.8s
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J)))))) (cbrt J))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(cbrt J)
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.1s

Calls
4 calls:
Slowest
369.0ms
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J)))))) (cbrt J))
281.0ms
(cbrt J)
230.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
220.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.2m

Calls
399 calls:
Slowest
1.0s
(* (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (sqrt (cos (/ K 2))) (* (sqrt -2) (* (sqrt (cbrt J)) (cbrt (sqrt J))))))) (cbrt (sqrt J)))
902.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J)))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J))))))) J)
861.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J)))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J))))))) (* (* (cbrt J) (cbrt J)) (cbrt J)))
836.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J)))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 (* (cbrt J) (cbrt J))))))) (* (* (cbrt J) (cbrt J)) (cbrt J)))
831.0ms
(* (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* (* (cbrt J) (cbrt J)) (cbrt J)) (* (* (cbrt J) (cbrt J)) (cbrt J))))))) (* (* (cbrt J) (cbrt J)) (cbrt J)))

prune4.4s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 3.8b

regimes356.0ms

Accuracy

0% (3.9b remaining)

Error of 7.6b against oracle of 3.7b and baseline of 7.6b

bsearch5.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.2s1516×body1280valid
1.6s4265×body80valid
1.5s1261×body640valid
491.0ms632×body320valid
148.0ms326×body160valid