Details

Time bar (total: 6.2s)

sample67.0ms

Algorithm
intervals
Results
26.0ms58×body1280valid
12.0ms39×body640valid
10.0ms138×body80valid
3.0ms14×body320valid
1.0ms7×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 16.4b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite35.0ms

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)
7.0ms
(sqrt (+ 1.0 (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))))

series498.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
128.0ms
(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)))
184.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify61.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04531006
11965898
25001898

prune257.0ms

Filtered
97 candidates to 62 candidates (63.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New89897
Fresh000
Picked101
Done000
Total90898

Merged error: 12.0b

Counts
98 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

rewrite34.0ms

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

series529.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
129.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
141.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
211.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0488988
12020866
25001866

prune219.0ms

Filtered
94 candidates to 59 candidates (62.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh077
Picked011
Done000
Total948102

Merged error: 12.0b

Counts
102 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite28.0ms

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))))
6.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
6.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
6.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
76.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
208.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
211.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03471291
112061104
250011096

prune331.0ms

Filtered
83 candidates to 63 candidates (75.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh066
Picked011
Done011
Total82991

Merged error: 12.0b

Counts
91 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
8.8b
(cbrt (pow (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
42×cbrt-prod
21×*-un-lft-identity
16×pow1 add-exp-log add-cbrt-cube
14×sqrt-prod
13×add-sqr-sqrt add-cube-cbrt
10×unpow-prod-down cube-prod
8×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×distribute-lft-out add-log-exp
3×flip3-+ pow1/3 flip-+
2×cube-div sqrt-div
1×cube-mult unpow3 associate-*r* associate-*l* *-commutative rem-cbrt-cube sqr-pow
Counts
4 → 87
Calls
4 calls:
6.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
10.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))
6.0ms
(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)))

series739.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
230.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))
221.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
210.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04621596
116361407
250021383

prune308.0ms

Filtered
99 candidates to 59 candidates (59.6%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New99099
Fresh066
Picked011
Done022
Total999108

Merged error: 12.0b

Counts
108 → 9

regimes287.0ms

Accuracy

87.5% (0.6b remaining)

Error of 13.6b against oracle of 13.0b and baseline of 18.0b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04950
14950

end0.0ms

sample1.8s

Algorithm
intervals
Results
684.0ms1520×body1280valid
392.0ms1249×body640valid
322.0ms4330×body80valid
142.0ms610×body320valid
45.0ms292×body160valid