Details

Time bar (total: 22.0s)

sample121.0ms

Algorithm
intervals
Results
46.0ms42×body640valid
28.0ms46×body1280valid
15.0ms132×body80valid
8.0ms21×body320valid
3.0ms15×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313224
418924
530024
673124
7246224
done500024

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite384.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
16×*-un-lft-identity
15×pow1
13×add-sqr-sqrt
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×sqrt-prod
7×unpow-prod-down associate-*r*
6×times-frac div-exp pow-prod-down
4×sqrt-div pow-exp add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative sqr-pow
Counts
4 → 90
Calls
4 calls:
18.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
38.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
231.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
209.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
280.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
237.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: 2 (455.0ms)

IterNodesCost
02142168
15311954
219531735
done50011735

prune459.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×add-cbrt-cube
18×pow1
14×prod-exp
12×*-un-lft-identity
11×add-sqr-sqrt cbrt-unprod
10×add-cube-cbrt
8×pow-prod-down
7×unpow-prod-down
6×times-frac div-exp
4×sqrt-div associate-*r/ pow-exp sqrt-prod add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ flip-+ div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* clear-num associate-/r* *-commutative distribute-lft-out sqr-pow
Counts
4 → 87
Calls
4 calls:
27.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
27.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
187.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
109.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series853.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
199.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
290.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
216.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: 2 (497.0ms)

IterNodesCost
02122138
15221929
218431679
done50011679

prune504.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
0.2b
(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
6.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
8.5b
(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
63×times-frac
38×*-un-lft-identity
37×add-sqr-sqrt
36×add-cube-cbrt
35×add-exp-log
25×unpow-prod-down add-cbrt-cube
18×pow1
10×div-exp prod-exp
9×cbrt-unprod div-inv
8×pow-prod-down
7×associate-/l*
5×cbrt-undiv
4×sqrt-div associate-*r/ pow-exp sqrt-prod add-log-exp
3×pow-unpow associate-/r*
2×flip3-+ flip-+
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* clear-num *-commutative associate-/l/ distribute-lft-out sqr-pow
Counts
4 → 130
Calls
4 calls:
15.0ms
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
29.0ms
(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
181.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
94.0ms
(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

series897.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
239.0ms
(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
313.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
194.0ms
(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

simplify1.4s

Counts
142 → 142
Iterations

Useful iterations: 2 (585.0ms)

IterNodesCost
02983126
17202885
221932633
done50002633

prune751.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.1b

localize22.0ms

Local error

Found 4 expressions with local error:

6.4b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.4b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite449.0ms

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:
101.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
133.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
102.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
107.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
286.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
364.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
197.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
206.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify3.0s

Counts
88 → 88
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0971968
11921666
24201604
311181598
434451592
done50001580

prune446.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.1b

regimes298.0ms

Accuracy

-20% (6.8b remaining)

Error of 18.9b against oracle of 12.1b and baseline of 17.7b

bsearch207.0ms

Steps
ItersRangePoint
9
-1.488607050460361e+122
-5.449253800430163e+114
-1.4686792642946565e+122
4
-4.94194543027164e+213
-3.284918449488842e+213
-3.44026472893723e+213

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03376
14653
done4653

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.7s1528×body1280valid
748.0ms1234×body640valid
578.0ms4294×body80valid
199.0ms610×body320valid
123.0ms335×body160valid