Details

Time bar (total: 6.6s)

sample65.0ms

Algorithm
intervals
Results
20.0ms43×body1280valid
11.0ms34×body640valid
10.0ms134×body80valid
8.0ms32×body320valid
2.0ms14×body160valid

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune4.0ms

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: 18.1b

Counts
2 → 1

localize22.0ms

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)
6.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite36.0ms

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:
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
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)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
130.0ms
(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))))
147.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify62.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
04531006
11965898
25001898

prune316.0ms

Filtered
97 candidates to 62 candidates (63.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New88997
Fresh000
Picked101
Done000
Total89998

Merged error: 13.2b

Counts
98 → 9

localize16.0ms

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)
6.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite38.0ms

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:
5.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
11.0ms
(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)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
142.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
191.0ms
(* (* -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)))

simplify61.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0488987
12021866
25002866

prune307.0ms

Filtered
94 candidates to 60 candidates (63.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New93194
Fresh088
Picked011
Done000
Total9310103

Merged error: 13.1b

Counts
103 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.8b
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
14.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×add-exp-log add-cbrt-cube
14×*-un-lft-identity
13×cbrt-prod
10×add-sqr-sqrt
8×add-cube-cbrt pow-prod-down prod-exp cbrt-unprod
7×sqrt-prod
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 71
Calls
4 calls:
7.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
11.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series759.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
82.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
225.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
224.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03471291
112061104
250011096

prune406.0ms

Filtered
83 candidates to 63 candidates (75.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New83083
Fresh088
Picked011
Done011
Total831093

Merged error: 13.1b

Counts
93 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
6.6b
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
29×add-exp-log
20×add-cbrt-cube
19×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 74
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
21.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (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)))

series640.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (cos (/ K 2.0)))
149.0ms
(cbrt (cos (/ K 2.0)))
195.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (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)))

simplify68.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04011337
118281008
25002913

prune285.0ms

Filtered
86 candidates to 56 candidates (65.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New85186
Fresh077
Picked101
Done022
Total861096

Merged error: 13.1b

Counts
96 → 10

regimes358.0ms

Accuracy

89.4% (0.6b remaining)

Error of 12.9b against oracle of 12.3b and baseline of 17.8b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05061
15061

end0.0ms

sample1.9s

Algorithm
intervals
Results
705.0ms1496×body1280valid
418.0ms1270×body640valid
335.0ms4285×body80valid
156.0ms647×body320valid
57.0ms305×body160valid