Details

Time bar (total: 44.9s)

sample179.0ms

Algorithm
intervals
Results
82.0ms54×body1280valid
39.0ms49×body640valid
24.0ms125×body80valid
11.0ms17×body320valid
4.0ms11×body160valid

simplify294.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
294.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize43.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (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)))

rewrite110.0ms

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
46.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
30.0ms
(* J (* (cos (/ K 2)) 2))
19.0ms
(* (cos (/ K 2)) (* -2 J))
14.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
105.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
61.0ms
(* (cos (/ K 2)) (* -2 J))
50.0ms
(* J (* (cos (/ K 2)) 2))

simplify7.0s

Counts
55 → 104
Calls
55 calls:
Slowest
837.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
540.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
456.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
368.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
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))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize41.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(/ U (* J (* (cos (/ K 2)) 2)))
0.1b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×associate-*l*
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp *-commutative associate-/l*
1×clear-num associate-/r* frac-2neg div-inv unswap-sqr
Counts
4 → 93
Calls
4 calls:
Slowest
36.0ms
(* J (* (cos (/ K 2)) 2))
27.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
27.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
16.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

series830.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
268.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
121.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
78.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.9s

Counts
58 → 105
Calls
58 calls:
Slowest
470.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
428.0ms
(* (* (* (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))))
420.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
341.0ms
(* (* (* (* (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 J) (* -2 J)) (* -2 J)))
340.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize54.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
0.1b
(/ (/ U J) (* (cos (/ K 2)) 2))
0.1b
(* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))
0.0b
(hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×pow1
13×associate-/l*
11×prod-exp cbrt-unprod
9×pow-prod-down
6×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×*-commutative
1×hypot-udef clear-num associate-/r* frac-2neg unswap-sqr associate-/l/
Counts
4 → 106
Calls
4 calls:
Slowest
30.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
13.0ms
(/ (/ U J) (* (cos (/ K 2)) 2))
8.0ms
(* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))
0.0ms
(hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2)))

series930.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
275.0ms
(* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))
267.0ms
(hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2)))
90.0ms
(/ (/ U J) (* (cos (/ K 2)) 2))

simplify6.8s

Counts
80 → 118
Calls
80 calls:
Slowest
354.0ms
(* (* (* (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))))
330.0ms
(- (- (log U) (log J)) (+ (log (cos (/ K 2))) (log 2)))
312.0ms
(* (* (* (* (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)))
307.0ms
(- (- (log U) (log J)) (log (* (cos (/ K 2)) 2)))
299.0ms
(* (* (* (* (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 J) (* -2 J)) (* -2 J)))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize53.0ms

Local error

Found 4 expressions with local error:

6.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.4b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (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))))) (* (cos (/ K 2)) (* -2 J)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
27×add-cbrt-cube add-exp-log
16×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*l* sqrt-prod
10×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 89
Calls
4 calls:
Slowest
170.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
52.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
348.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
317.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
249.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
243.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify7.6s

Counts
55 → 101
Calls
55 calls:
Slowest
501.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
485.0ms
(* (* (* (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)))))
393.0ms
(* (* (* (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)))))
392.0ms
(* (* (* (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)))))
351.0ms
(* (* (* (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)))))

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

regimes510.0ms

Accuracy

0% (3.9b remaining)

Error of 7.8b against oracle of 3.9b and baseline of 7.8b

bsearch5.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.1s1541×body1280valid
1.7s1307×body640valid
1.1s4262×body80valid
403.0ms590×body320valid
163.0ms305×body160valid