Details

Time bar (total: 14.0s)

sample120.0ms

Algorithm
intervals
Results
44.0ms46×body1280valid
21.0ms49×body640valid
14.0ms134×body80valid
7.0ms18×body320valid
5.0ms10×body160valid

simplify123.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize20.0ms

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
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite484.0ms

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:
35.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
42.0ms
(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)))
294.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
196.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
195.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
345.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify64.0ms

Counts
97 → 97

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.4b

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)
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

rewrite419.0ms

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/ associate-*r* pow-exp 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:
34.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
47.0ms
(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)))
228.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series859.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
249.0ms
(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)))
310.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify70.0ms

Counts
94 → 94

prune477.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.4b

localize35.0ms

Local error

Found 4 expressions with local error:

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)))
9.5b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.5b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite426.0ms

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:
97.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
90.0ms
(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))))
129.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
185.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
211.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
383.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
357.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify114.0ms

Counts
88 → 88

prune677.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.4b

localize61.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite813.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1
31×add-exp-log add-cbrt-cube
21×associate-*r*
19×*-un-lft-identity
18×pow-prod-down prod-exp cbrt-unprod
16×sqrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt
8×sqrt-div
6×associate-*r/
4×flip3-+ flip-+ distribute-lft-out add-log-exp
3×associate-*l* *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 97
Calls
4 calls:
106.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
242.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
226.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
235.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
219.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
288.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
317.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
252.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify50.0ms

Counts
109 → 109

prune585.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 13.4b

regimes917.0ms

Accuracy

90.1% (0.5b remaining)

Error of 13.2b against oracle of 12.7b and baseline of 18.1b

bsearch2.0ms

simplify86.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s1537×body1280valid
736.0ms4277×body80valid
691.0ms1247×body640valid
356.0ms613×body320valid
83.0ms330×body160valid