Details

Time bar (total: 6.9s)

sample82.0ms

Algorithm
intervals
Results
29.0ms45×body1280valid
19.0ms43×body640valid
13.0ms143×body80valid
6.0ms19×body320valid
1.0ms6×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.6b

Counts
2 → 1

localize16.0ms

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)
8.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite40.0ms

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)
17.0ms
(* (* (* -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)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
136.0ms
(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))))
138.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05431085
12466960
25002960

prune280.0ms

Filtered
102 candidates to 67 candidates (65.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New966102
Fresh000
Picked011
Done000
Total967103

Merged error: 13.4b

Counts
103 → 7

localize22.0ms

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)
8.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

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))))
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)))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
139.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
188.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
140.0ms
(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 (14.0ms)

IterNodesCost
05371066
12238928
25001928

prune243.0ms

Filtered
99 candidates to 64 candidates (64.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh055
Picked011
Done011
Total997106

Merged error: 13.4b

Counts
106 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite36.0ms

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:
14.0ms
(* (* (* -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)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
142.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
146.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
144.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02541060
11124971
25001961

prune293.0ms

Filtered
87 candidates to 58 candidates (66.7%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New87087
Fresh044
Picked011
Done022
Total87794

Merged error: 13.4b

Counts
94 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0)
8.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0))))
8.9b
(sqrt (+ 1.0 (pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0)))
26.1b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
40×cbrt-prod
37×unpow-prod-down
23×*-un-lft-identity
20×add-sqr-sqrt
19×add-cube-cbrt
15×pow1
14×add-exp-log cube-prod
13×add-cbrt-cube
12×times-frac
8×sqrt-prod
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×sqrt-div div-inv add-log-exp
3×pow-unpow sqr-pow
2×cube-mult pow-pow flip3-+ pow1/3 unpow3 associate-*r/ flip-+ distribute-lft-out
1×cube-div pow-to-exp rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 associate-*l* pow-exp *-commutative rem-cbrt-cube
Counts
4 → 111
Calls
4 calls:
7.0ms
(pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0)
19.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0))))
13.0ms
(sqrt (+ 1.0 (pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0)))
5.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3))

series567.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0)
189.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0))))
138.0ms
(sqrt (+ 1.0 (pow (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3)) 2.0)))
96.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 3))

simplify80.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05901544
126371441
250011433

prune283.0ms

Filtered
123 candidates to 66 candidates (53.7%)
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New1230123
Fresh033
Picked011
Done033
Total1237130

Merged error: 13.4b

Counts
130 → 7

regimes270.0ms

Accuracy

75% (1.3b remaining)

Error of 14.1b against oracle of 12.8b and baseline of 18.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.2s1480×body1280valid
557.0ms1221×body640valid
388.0ms4346×body80valid
210.0ms634×body320valid
68.0ms322×body160valid