Details

Time bar (total: 46.1s)

sample117.0ms

Algorithm
intervals
Results
35.0ms155×body80valid
34.0ms42×body1280valid
21.0ms36×body640valid
7.0ms15×body320valid
3.0ms9×body160valid

simplify621.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
621.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize33.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (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)))

rewrite91.0ms

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
45.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
19.0ms
(* J (* (cos (/ K 2)) 2))
14.0ms
(* (cos (/ K 2)) (* -2 J))
12.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
331.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
117.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
69.0ms
(* (cos (/ K 2)) (* -2 J))
61.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.8s

Counts
55 → 104
Calls
55 calls:
Slowest
512.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
425.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
411.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
401.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))
379.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize52.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (* (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)))
0.0b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

rewrite126.0ms

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
56.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
28.0ms
(* J (* (cos (/ K 2)) 2))
26.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
15.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

series840.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
354.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
293.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
125.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
68.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.7s

Counts
58 → 105
Calls
58 calls:
Slowest
488.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
390.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
381.0ms
(* (* (* (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))))
355.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
308.0ms
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize31.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
0.1b
(/ (/ U J) (* (cos (/ K 2)) 2))
0.0b
(* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))
0.0b
(hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2)))

rewrite64.0ms

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
38.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
13.0ms
(* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))
10.0ms
(/ (/ U J) (* (cos (/ K 2)) 2))
0.0ms
(hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2)))

series972.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
261.0ms
(* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))
259.0ms
(hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2)))
124.0ms
(/ (/ U J) (* (cos (/ K 2)) 2))

simplify6.9s

Counts
80 → 118
Calls
80 calls:
Slowest
342.0ms
(* (* (* (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))))
307.0ms
(/ (* (* (/ U J) (/ U J)) (/ U J)) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
305.0ms
(- (- (log U) (log J)) (+ (log (cos (/ K 2))) (log 2)))
275.0ms
(/ (/ (* (* U U) U) (* (* J J) J)) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
274.0ms
(* (* (* (* (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

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize60.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
7.8b
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
7.8b
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
0.5b
(cbrt (* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
40×pow1 add-cbrt-cube add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* *-commutative
1×cbrt-prod pow1/3
Counts
4 → 87
Calls
4 calls:
Slowest
50.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
49.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
49.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
26.0ms
(cbrt (* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J)))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
487.0ms
(cbrt (* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J)))
395.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
361.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))
313.0ms
(* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* -2 J))

simplify8.3s

Counts
52 → 99
Calls
52 calls:
Slowest
687.0ms
(* (* (* (* (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)))
397.0ms
(* (cbrt -2) (exp (* 1/3 (- (log 1/2) (log (/ 1 U))))))
314.0ms
(* (* (* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))) (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
301.0ms
(* (* (* (* (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)))
289.0ms
(* (* (* (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2))) (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))) (* (hypot 1 (/ (/ U J) (* (cos (/ K 2)) 2))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.0b

regimes471.0ms

Accuracy

0% (3.4b remaining)

Error of 7.0b against oracle of 3.6b and baseline of 7.0b

bsearch3.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.4s1468×body1280valid
1.3s1235×body640valid
1.3s4356×body80valid
441.0ms630×body320valid
138.0ms317×body160valid