Details

Time bar (total: 6.6s)

sample112.0ms

Algorithm
intervals
Results
45.0ms59×body1280valid
21.0ms38×body640valid
14.0ms127×body80valid
8.0ms20×body320valid
3.0ms13×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.2b

Counts
2 → 1

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)
5.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
5.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite33.0ms

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)
6.0ms
(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))))

series120.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
32.0ms
(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)))
45.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify59.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04531006
11965898
25001898

prune240.0ms

Filtered
97 candidates to 62 candidates (36.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh000
Picked011
Done000
Total89998

Merged error: 8.1b

Counts
98 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (* (pow (* (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0))))) (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))) 2.0) (pow (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)))))
16.7b
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))
16.7b
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))
16.7b
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
13×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div associate-*r/
1×flip3-+ associate-*l* *-commutative flip-+
Counts
4 → 74
Calls
4 calls:
9.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (* (pow (* (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0))))) (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))) 2.0) (pow (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)))))
5.0ms
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))
5.0ms
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))
5.0ms
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))

series202.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (* (pow (* (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0))))) (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))) 2.0) (pow (cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)))))
36.0ms
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))
34.0ms
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))
34.0ms
(cbrt (/ U (* (* 2.0 J) (cos (/ K 2.0)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04241529
116561356
250011348

prune434.0ms

Filtered
86 candidates to 71 candidates (17.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New84286
Fresh077
Picked011
Done011
Total841195

Merged error: 8.1b

Counts
95 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
5.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
5.2b
(* (* (* (* -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))))

rewrite34.0ms

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)))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms
(* (* (* (* -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))))

series115.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(cbrt (cos (/ K 2.0)))
20.0ms
(cbrt (cos (/ K 2.0)))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
43.0ms
(* (* (* (* -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))))

simplify62.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04041335
118501000
25002911

prune299.0ms

Filtered
86 candidates to 52 candidates (39.5%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New80686
Fresh088
Picked101
Done022
Total811697

Merged error: 8.0b

Counts
97 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
5.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
5.3b
(* (* (* -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)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
46×pow1
45×add-exp-log
32×add-cbrt-cube
31×pow-prod-down prod-exp cbrt-unprod
9×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-prod
4×sqrt-div associate-*r/ sqrt-prod add-log-exp
2×flip3-+ pow1/3 flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative distribute-lft-out
Counts
4 → 80
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
19.0ms
(* (* (* -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)))))

series115.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(cbrt (cos (/ K 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))
37.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
44.0ms
(* (* (* -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)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04141576
117821181
250011027

prune206.0ms

Filtered
92 candidates to 50 candidates (45.7%)
Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New91192
Fresh11213
Picked011
Done022
Total9216108

Merged error: 8.0b

Counts
108 → 16

regimes853.0ms

Accuracy

90.5% (0.4b remaining)

Error of 10.3b against oracle of 9.9b and baseline of 14.4b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04550
14550

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s1628×body1280valid
716.0ms1271×body640valid
654.0ms4119×body80valid
261.0ms637×body320valid
91.0ms347×body160valid

Profiling

Loading profile data...