Details

Time bar (total: 25.5s)

sample107.0ms

Algorithm
intervals
Results
30.0ms46×body1280valid
22.0ms144×body80valid
22.0ms45×body640valid
5.0ms15×body320valid
2.0ms6×body160valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
017636
134636
271636
3135636
4208636
5492636
63236636
done5000636

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* associate-*r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
29.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
35.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
168.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
65.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series808.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
221.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
289.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
233.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.5s

Counts
97 → 97
Iterations

Useful iterations: 2 (766.0ms)

IterNodesCost
019249466
150846615
2236846095
done500246095

prune677.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r* pow-exp associate-*r/ sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
16.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
18.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
104.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
60.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series739.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
245.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
244.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
167.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.1s

Counts
94 → 94
Iterations

Useful iterations: done (2.1s)

IterNodesCost
019948414
154445706
2242744986
done500244946

prune611.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.9b

localize84.0ms

Local error

Found 4 expressions with local error:

1.7b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.8b
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
16.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×cbrt-prod add-cbrt-cube add-exp-log
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*l* *-commutative
Counts
4 → 70
Calls
4 calls:
99.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
45.0ms
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
30.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
49.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
301.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
151.0ms
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
336.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
357.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.2s

Counts
82 → 82
Iterations

Useful iterations: done (2.2s)

IterNodesCost
015762963
136757626
2155556946
done500156226

prune750.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.9b

localize108.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.8b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-cbrt-cube add-exp-log
11×cbrt-prod
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
6×pow-prod-down prod-exp cbrt-unprod
4×cbrt-div sqrt-div add-log-exp
3×flip3-+ associate-*r* flip-+ distribute-lft-out
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 68
Calls
4 calls:
75.0ms
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
49.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
60.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
41.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
342.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
228.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
355.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.8s

Counts
80 → 80
Iterations

Useful iterations: done (2.8s)

IterNodesCost
017160724
139355900
2166255540
done500054860

prune734.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 14.9b

regimes500.0ms

Accuracy

0% (5.5b remaining)

Error of 18.5b against oracle of 13.0b and baseline of 18.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
017636
123636
done23636

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s1520×body1280valid
782.0ms1296×body640valid
696.0ms4242×body80valid
551.0ms324×body160valid
245.0ms623×body320valid