Details

Time bar (total: 22.8s)

sample129.0ms

Algorithm
intervals
Results
39.0ms52×body1280valid
28.0ms127×body80valid
26.0ms46×body640valid
9.0ms20×body320valid
3.0ms11×body160valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313524
420624
549124
6330124
done500024

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize23.0ms

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)
7.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite462.0ms

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-*r/ associate-*l* *-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:
25.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
45.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
284.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
104.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series731.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
215.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
255.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
196.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.7s

Counts
97 → 97
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01932013
15081800
223991625
done50001613

prune470.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.9b

localize24.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
11.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite782.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
29×pow1
25×add-exp-log add-cbrt-cube
20×sqrt-prod
15×pow-prod-down prod-exp cbrt-unprod
14×*-un-lft-identity
12×add-sqr-sqrt
10×associate-*r/
9×flip3-+ flip-+
8×add-cube-cbrt
6×sqrt-pow1
4×frac-times rem-sqrt-square pow1/2 add-log-exp
3×distribute-lft-out
2×associate-*l/
1×associate-*r* associate-*l* *-commutative
Counts
4 → 90
Calls
4 calls:
85.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
452.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
101.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
135.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
369.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
311.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
191.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
225.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01683653
14162459
214702198
done50012196

prune578.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 14.9b

localize57.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite424.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
131.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
104.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
93.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
91.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
355.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
316.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
220.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
219.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.0s

Counts
88 → 88
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0971968
11951666
24701604
314521598
done50011592

prune959.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
19.6b
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) 1/4)

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×sqrt-prod
15×add-exp-log add-sqr-sqrt
12×add-cube-cbrt
11×unpow-prod-down
9×pow1
6×pow-unpow sqrt-div
5×sqrt-pow1 pow-exp
4×add-cbrt-cube add-log-exp
3×rem-sqrt-square times-frac pow1/2 div-exp prod-exp distribute-lft-out
2×pow-to-exp pow-pow flip3-+ flip-+ sqr-pow
1×div-inv
Counts
4 → 80
Calls
4 calls:
22.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
91.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
76.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
128.0ms
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) 1/4)

series1.1s

Counts
4 → 12
Calls
4 calls:
203.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
382.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
202.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
326.0ms
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) 1/4)

simplify2.2s

Counts
92 → 92
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01921927
14711706
213951651
348901645
done50021645

prune552.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 14.9b

regimes464.0ms

Accuracy

82.2% (0.9b remaining)

Error of 14.0b against oracle of 13.1b and baseline of 18.3b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.3s1542×body1280valid
929.0ms4308×body80valid
687.0ms1218×body640valid
284.0ms619×body320valid
72.0ms317×body160valid