Details

Time bar (total: 10.3s)

analyze1.9s

Algorithm
search

sample108.0ms

Algorithm
intervals
Results
40.0ms50×body1280valid
31.0ms56×body640valid
13.0ms118×body80valid
8.0ms21×body320valid
3.0ms11×body160valid
0.0ms1×body80invalid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.7b

Counts
2 → 1

localize17.0ms

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)
6.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

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:
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
13.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series124.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
31.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify69.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05431085
12466960
25002960

prune240.0ms

Filtered
67 candidates to 102 candidates (-52.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New957102
Fresh000
Picked011
Done000
Total958103

Merged error: 12.0b

Counts
103 → 8

localize17.0ms

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)
6.9b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite36.0ms

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:
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
12.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series127.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
33.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
42.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify63.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05371066
12238928
25001928

prune220.0ms

Filtered
64 candidates to 99 candidates (-54.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New97299
Fresh066
Picked101
Done011
Total989107

Merged error: 12.0b

Counts
107 → 9

localize16.0ms

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)
6.9b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
9.6b
(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

rewrite52.0ms

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:
7.0ms
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
9.0ms
(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
20.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
12.0ms
(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

series128.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
31.0ms
(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
46.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
34.0ms
(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
07391616
129801477
250011477

prune415.0ms

Filtered
103 candidates to 142 candidates (-37.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1420142
Fresh077
Picked011
Done011
Total1429151

Merged error: 12.0b

Counts
151 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×pow1 sqrt-prod
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-div
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×flip3-+ flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*r/
1×associate-*l* *-commutative
Counts
4 → 75
Calls
4 calls:
13.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series174.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
48.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
35.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02541060
11124971
25001961

prune430.0ms

Filtered
58 candidates to 87 candidates (-50.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New86187
Fresh066
Picked011
Done022
Total861096

Merged error: 12.0b

Counts
96 → 10

regimes680.0ms

Accuracy

92.3% (0.4b remaining)

Error of 13.7b against oracle of 13.3b and baseline of 18.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

analyze2.1s

Algorithm
search

sample3.1s

Algorithm
intervals
Results
1.3s1476×body1280valid
741.0ms1286×body640valid
494.0ms4257×body80valid
274.0ms670×body320valid
90.0ms311×body160valid
0.0ms3×body80invalid

Profiling

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