Details

Time bar (total: 2.0m)

sample225.0ms

Algorithm
intervals
Results
94.0ms53×body1280valid
45.0ms38×body640valid
41.0ms140×body80valid
13.0ms15×body320valid
7.0ms10×body160valid

simplify658.0ms

Calls
1 calls:
Slowest
658.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize43.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (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)))

rewrite221.0ms

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
104.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
43.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
42.0ms
(* J (* (cos (/ K 2)) 2))
28.0ms
(* (cos (/ K 2)) (* -2 J))

series584.0ms

Calls
4 calls:
Slowest
336.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
117.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
67.0ms
(* (cos (/ K 2)) (* -2 J))
65.0ms
(* J (* (cos (/ K 2)) 2))

simplify14.7s

Calls
250 calls:
Slowest
476.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
471.0ms
(* (* (* 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))))
399.0ms
(/ (* (cbrt U) (cbrt U)) (* J (* (cos (/ K 2)) (* (cbrt 2) (cbrt 2)))))
399.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))

prune3.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 4 expressions with local error:

6.2b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.2b
(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
(* J (* (cos (/ K 2)) 2))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
52×associate-*r*
51×add-sqr-sqrt
20×pow1 unswap-sqr
18×add-cbrt-cube associate-*l* add-exp-log
17×*-un-lft-identity add-cube-cbrt
12×sqrt-prod
9×pow-prod-down prod-exp cbrt-unprod
5×*-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
116.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
47.0ms
(* 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)))))

series880.0ms

Calls
4 calls:
Slowest
344.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
240.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
233.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
63.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.0s

Calls
89 calls:
Slowest
485.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
394.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
304.0ms
(* (* (* (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)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J))))
295.0ms
(* (* (* (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))))
255.0ms
(* (* (* (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)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J))))

prune2.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (* -2 J)))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
291×add-sqr-sqrt
199×unswap-sqr
113×add-cbrt-cube
111×cbrt-unprod
86×cbrt-prod
75×associate-*r*
62×associate-*l*
40×pow1 add-exp-log
27×pow-prod-down prod-exp
24×*-un-lft-identity add-cube-cbrt
18×swap-sqr
11×*-commutative
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
Calls
4 calls:
Slowest
262.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (* -2 J)))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))

series814.0ms

Calls
4 calls:
Slowest
335.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (* -2 J)))
171.0ms
(cbrt (cos (/ K 2)))
165.0ms
(cbrt (cos (/ K 2)))
143.0ms
(cbrt (cos (/ K 2)))

simplify53.4s

Calls
235 calls:
Slowest
844.0ms
(* (* (* (* (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)))))) (* (cos (/ K 2)) (* (* (* -2 J) (* -2 J)) (* -2 J))))
714.0ms
(* (* (* (* (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))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))) (* (* (* -2 -2) -2) (* (* J J) J))))
704.0ms
(* (* (* (* (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))) (cbrt (cos (/ K 2)))) (cbrt (cos (/ K 2)))) (* (* (* -2 -2) -2) (* (* J J) J))))
644.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
637.0ms
(* (* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 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))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J))))

prune3.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.1b

localize14.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* -2 J))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
129×add-sqr-sqrt
74×unswap-sqr
56×associate-*l*
48×associate-*r*
44×add-cbrt-cube
43×cbrt-prod
36×cbrt-unprod
25×pow1 add-exp-log
21×*-un-lft-identity add-cube-cbrt
15×pow-prod-down prod-exp
12×swap-sqr
7×*-commutative
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
Calls
4 calls:
Slowest
219.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* -2 J))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))

series980.0ms

Calls
4 calls:
Slowest
478.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* -2 J))
174.0ms
(cbrt (cos (/ K 2)))
167.0ms
(cbrt (cos (/ K 2)))
161.0ms
(cbrt (cos (/ K 2)))

simplify21.0s

Calls
136 calls:
Slowest
480.0ms
(* (* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))) (* (* (* -2 -2) -2) (* (* J J) J)))
430.0ms
(* (* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
423.0ms
(* (* (* (* (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)))))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
414.0ms
(* (* (* (* (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)))))) (* (* (* -2 -2) -2) (* (* J J) J)))
402.0ms
(* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (cbrt (cos (/ K 2)))) (cbrt (sqrt (cos (/ K 2)))))) (* (sqrt -2) (sqrt J)))

prune2.6s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.1b

regimes578.0ms

Accuracy

0% (3.9b remaining)

Error of 7.7b against oracle of 3.9b and baseline of 7.7b

bsearch5.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.3s1538×body1280valid
1.8s1229×body640valid
1.3s4291×body80valid
962.0ms615×body320valid
230.0ms328×body160valid