Details

Time bar (total: 9.7s)

analyze1.9s

Algorithm
search

sample94.0ms

Algorithm
intervals
Results
35.0ms42×body1280valid
21.0ms38×body640valid
16.0ms147×body80valid
7.0ms17×body320valid
3.0ms12×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.2b

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)
6.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite32.0ms

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)))
6.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
12.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (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)))

series111.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
29.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
42.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
32.0ms
(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 (10.0ms)

IterNodesCost
04531006
11965898
25001898

prune230.0ms

Filtered
62 candidates to 97 candidates (-56.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New88997
Fresh000
Picked101
Done000
Total89998

Merged error: 13.9b

Counts
98 → 9

localize15.0ms

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)
6.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
11.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite31.0ms

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)))
6.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
12.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (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)))

series110.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
30.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
39.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify54.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0488987
12021866
25002866

prune217.0ms

Filtered
60 candidates to 94 candidates (-56.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New93194
Fresh088
Picked011
Done000
Total9310103

Merged error: 13.9b

Counts
103 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.5b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite29.0ms

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:
7.0ms
(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))))
6.0ms
(sqrt (+ 1.0 (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)))

series184.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
57.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
33.0ms
(sqrt (+ 1.0 (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)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune338.0ms

Filtered
62 candidates to 88 candidates (-41.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh088
Picked011
Done011
Total881098

Merged error: 13.9b

Counts
98 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

6.5b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
11.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
29×pow1
25×add-exp-log add-cbrt-cube
20×sqrt-prod
18×associate-*r/
15×pow-prod-down prod-exp cbrt-unprod
14×*-un-lft-identity
12×add-sqr-sqrt
9×flip3-+ flip-+
8×add-cube-cbrt
6×sqrt-pow1
4×frac-times rem-sqrt-square pow1/2 add-log-exp
3×distribute-lft-out
2×associate-*l/
1×associate-*r* associate-*l* *-commutative
Counts
4 → 90
Calls
4 calls:
7.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
28.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (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)))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series163.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
44.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
31.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
32.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
04371680
114731360
250011360

prune316.0ms

Filtered
67 candidates to 102 candidates (-52.2%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1020102
Fresh077
Picked011
Done022
Total10210112

Merged error: 13.9b

Counts
112 → 10

regimes527.0ms

Accuracy

92.1% (0.4b remaining)

Error of 13.4b against oracle of 12.9b and baseline of 18.6b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04950
14950

end0.0ms

analyze1.9s

Algorithm
search

sample3.1s

Algorithm
intervals
Results
1.3s1466×body1280valid
750.0ms1262×body640valid
506.0ms4336×body80valid
271.0ms629×body320valid
88.0ms307×body160valid
1.0ms1×body1280invalid
0.0ms3×body80invalid

Profiling

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