Details

Time bar (total: 25.0s)

sample170.0ms

Algorithm
intervals
Results
49.0ms53×body640valid
45.0ms40×body1280valid
35.0ms133×body80valid
10.0ms16×body320valid
6.0ms14×body160valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done2093
52093
4843
3216
285
136
017

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.4b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

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 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
Counts
4 → 92
Calls
4 calls:
29.0ms
(/ U (* (* 2 J) (cos (/ K 2))))
26.0ms
(* (cos (/ K 2)) (* -2 J))
19.0ms
(* (* 2 J) (cos (/ K 2)))
53.0ms
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ U (* (* 2 J) (cos (/ K 2))))
70.0ms
(* (cos (/ K 2)) (* -2 J))
66.0ms
(* (* 2 J) (cos (/ K 2)))
370.0ms
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.5s

Counts
104 → 104
Iterations
IterNodes
done2090
32090
21564
1413
0161

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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-*r*
5×associate-*l*
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:
14.0ms
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2)))
19.0ms
(/ U (* (* 2 J) (cos (/ K 2))))
16.0ms
(* (* 2 J) (cos (/ K 2)))
31.0ms
(* (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

series817.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2)))
125.0ms
(/ U (* (* 2 J) (cos (/ K 2))))
77.0ms
(* (* 2 J) (cos (/ K 2)))
368.0ms
(* (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

simplify1.4s

Counts
105 → 105
Iterations
IterNodes
done2012
32012
21550
1405
0159

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2))))
0.1b
(* (hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2)))) (cos (/ K 2)))
0.1b
(/ (/ (/ U 2) J) (cos (/ K 2)))
7.4b
(* (* (hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2)))) (cos (/ K 2))) (* -2 J))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
393×times-frac
192×add-sqr-sqrt
190×*-un-lft-identity add-cube-cbrt
43×associate-/l*
27×add-cbrt-cube add-exp-log
18×pow1
17×div-inv
9×pow-prod-down prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×*-commutative
1×hypot-udef clear-num frac-2neg unswap-sqr associate-/l/
Counts
4 → 252
Calls
4 calls:
0.0ms
(hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2))))
7.0ms
(* (hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2)))) (cos (/ K 2)))
12.0ms
(/ (/ (/ U 2) J) (cos (/ K 2)))
35.0ms
(* (* (hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2)))) (cos (/ K 2))) (* -2 J))

series934.0ms

Counts
4 → 12
Calls
4 calls:
301.0ms
(hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2))))
205.0ms
(* (hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2)))) (cos (/ K 2)))
138.0ms
(/ (/ (/ U 2) J) (cos (/ K 2)))
290.0ms
(* (* (hypot 1 (/ (/ (/ U 2) J) (cos (/ K 2)))) (cos (/ K 2))) (* -2 J))

simplify1.5s

Counts
264 → 264
Iterations
IterNodes
done2000
22000
11193
0528

prune3.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))
7.4b
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log
23×add-cbrt-cube
22×pow-prod-down prod-exp cbrt-unprod
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* *-commutative
Counts
4 → 78
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))
194.0ms
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(cbrt (cos (/ K 2)))
146.0ms
(cbrt (cos (/ K 2)))
142.0ms
(cbrt (cos (/ K 2)))
341.0ms
(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify1.8s

Counts
90 → 90
Iterations
IterNodes
done2000
32000
21283
1327
0123

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

regimes525.0ms

Accuracy

0% (4.0b remaining)

Error of 7.7b against oracle of 3.7b and baseline of 7.7b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done20
120
015

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.9s1482×body1280valid
1.6s1300×body640valid
1.2s4273×body80valid
553.0ms628×body320valid
132.0ms320×body160valid