Details

Time bar (total: 7.5s)

sample115.0ms

Algorithm
intervals
Results
47.0ms58×body1280valid
24.0ms41×body640valid
16.0ms133×body80valid
7.0ms15×body320valid
2.0ms9×body160valid

simplify58.0ms

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: 16.7b

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)
7.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite48.0ms

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:
11.0ms
(/ U (* (* 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)))
18.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
146.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
150.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
261.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify81.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05431085
12466960
25002960

prune392.0ms

Filtered
102 candidates to 67 candidates (65.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New957102
Fresh000
Picked011
Done000
Total958103

Merged error: 10.6b

Counts
103 → 8

localize19.0ms

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)
7.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.1b
(* (* -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
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)
6.0ms
(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)))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
126.0ms
(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)))
188.0ms
(* (* -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
99 → 99
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05371066
12238928
25001928

prune243.0ms

Filtered
99 candidates to 63 candidates (63.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New98199
Fresh066
Picked011
Done011
Total989107

Merged error: 10.6b

Counts
107 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
14.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite31.0ms

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:
11.0ms
(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)))

series725.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
77.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
216.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
216.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03471291
112061104
250011096

prune333.0ms

Filtered
83 candidates to 63 candidates (75.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New81283
Fresh066
Picked011
Done022
Total811192

Merged error: 10.5b

Counts
92 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

14.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-prod *-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 56
Calls
4 calls:
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)))
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)))

series874.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
216.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
217.0ms
(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)))

simplify44.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
0150968
1344900
21231884
35002872

prune343.0ms

Filtered
68 candidates to 60 candidates (88.2%)
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New68068
Fresh077
Picked011
Done033
Total681179

Merged error: 10.5b

Counts
79 → 11

regimes362.0ms

Accuracy

84.9% (0.8b remaining)

Error of 13.4b against oracle of 12.5b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04661
14661

end0.0ms

sample2.4s

Algorithm
intervals
Results
950.0ms1521×body1280valid
571.0ms1252×body640valid
395.0ms4338×body80valid
190.0ms593×body320valid
70.0ms299×body160valid