Details

Time bar (total: 6.9s)

sample80.0ms

Algorithm
intervals
Results
27.0ms44×body1280valid
17.0ms40×body640valid
12.0ms139×body80valid
7.0ms23×body320valid
2.0ms10×body160valid

simplify47.0ms

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: 19.4b

Counts
2 → 1

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)
7.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.0b
(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)
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)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
127.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
183.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04531006
11965898
25001898

prune265.0ms

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: 12.7b

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)
7.2b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
11.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

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)
16.0ms
(* (* -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)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
136.0ms
(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)))))
139.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0488987
12021866
25002866

prune248.0ms

Filtered
94 candidates to 60 candidates (63.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh088
Picked011
Done000
Total949103

Merged error: 12.7b

Counts
103 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.2b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

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:
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0ms
(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)))

series739.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
214.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
161.0ms
(sqrt (+ 1.0 (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)))

simplify58.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune312.0ms

Filtered
88 candidates to 62 candidates (70.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh077
Picked011
Done011
Total88997

Merged error: 12.7b

Counts
97 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
0.9b
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
17.7b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
17.7b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite29.0ms

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))))))
7.0ms
(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)))

series743.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(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))))))
223.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
219.0ms
(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 (35.0ms)

IterNodesCost
03471291
112061104
250011096

prune316.0ms

Filtered
83 candidates to 63 candidates (75.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New82183
Fresh066
Picked011
Done022
Total821092

Merged error: 12.7b

Counts
92 → 10

regimes326.0ms

Accuracy

64% (1.9b remaining)

Error of 14.5b against oracle of 12.6b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04950
14950

end0.0ms

sample2.4s

Algorithm
intervals
Results
941.0ms1500×body1280valid
572.0ms1261×body640valid
392.0ms4300×body80valid
204.0ms632×body320valid
65.0ms309×body160valid

Profiling

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