Details

Time bar (total: 20.0s)

sample173.0ms

Algorithm
intervals
Results
53.0ms40×body1280valid
42.0ms42×body640valid
37.0ms146×body80valid
9.0ms13×body320valid
7.0ms15×body160valid

simplify1.0s

Counts
1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize53.0ms

Local error

Found 4 expressions with local error:

7.6b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.1b
(/ U (* J (* (cos (/ K 2)) 2)))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(* (cos (/ K 2)) (* -2 J))

rewrite102.0ms

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
47.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
21.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
18.0ms
(* (cos (/ K 2)) (* -2 J))
14.0ms
(* J (* (cos (/ K 2)) 2))

series630.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
367.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
111.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
88.0ms
(* (cos (/ K 2)) (* -2 J))
64.0ms
(* J (* (cos (/ K 2)) 2))

simplify554.0ms

Counts
105 → 104

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

localize50.0ms

Local error

Found 4 expressions with local error:

7.6b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b
(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
(/ U (* J (* (cos (/ K 2)) 2)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube add-exp-log
15×pow1
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×prod-exp sqrt-prod cbrt-unprod
6×associate-*l* pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×clear-num associate-/r* frac-2neg associate-*r* *-commutative div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
63.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
19.0ms
(/ 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)))))

series962.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
356.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
262.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
236.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
107.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

simplify530.0ms

Counts
102 → 97

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize57.0ms

Local error

Found 4 expressions with local error:

7.6b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b
(sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))
0.2b
(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
0.2b
(* (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
27×add-cbrt-cube
25×prod-exp
17×pow1
15×add-sqr-sqrt
13×cbrt-unprod
11×*-un-lft-identity add-cube-cbrt
9×associate-*l* sqrt-prod
8×associate-*r*
7×pow-prod-down
6×div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp times-frac 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
1×associate-*r/ un-div-inv div-inv unswap-sqr
Counts
4 → 98
Calls
4 calls:
Slowest
74.0ms
(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
62.0ms
(* (sqrt (hypot 1 (* U (/ 1 (* 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 (/ 1 (* J (* (cos (/ K 2)) 2))))))

series924.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(* (sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))
260.0ms
(sqrt (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))))
243.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
122.0ms
(* U (/ 1 (* J (* (cos (/ K 2)) 2))))

simplify654.0ms

Counts
110 → 110

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.5b

localize78.0ms

Local error

Found 4 expressions with local error:

7.6b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
7.6b
(sqrt (hypot 1 (* (* U (* (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))))
0.6b
(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
0.6b
(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 times-frac sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 pow1/3 div-inv
Counts
4 → 70
Calls
4 calls:
Slowest
16.0ms
(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
14.0ms
(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (* (* U (* (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
470.0ms
(sqrt (hypot 1 (* (* U (* (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))) (cbrt (/ 1 (* J (* (cos (/ K 2)) 2)))))))
260.0ms
(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))
254.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
208.0ms
(cbrt (/ 1 (* J (* (cos (/ K 2)) 2))))

simplify457.0ms

Counts
98 → 82

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.5b

regimes451.0ms

Accuracy

0% (3.7b remaining)

Error of 7.8b against oracle of 4.0b and baseline of 7.8b

bsearch3.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.0s1515×body1280valid
1.7s1237×body640valid
982.0ms4296×body80valid
411.0ms602×body320valid
160.0ms352×body160valid