Details

Time bar (total: 11.0s)

sample2.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results
34.0ms41×body1280valid
23.0ms40×body640valid
21.0ms150×body80valid
6.0ms16×body320valid
2.0ms9×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.2b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b
(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)
13.0ms
(* (* (* -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)))

series121.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
33.0ms
(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))))
38.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04531006
11965898
25001898

prune251.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New871097
Fresh000
Picked101
Done000
Total881098

Merged error: 12.4b

Counts
98 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.3b
(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)))))
8.9b
(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)
12.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series119.0ms

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)
45.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0488987
12021866
25002866

prune228.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh099
Picked011
Done000
Total9410104

Merged error: 12.4b

Counts
104 → 10

localize19.0ms

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))))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite30.0ms

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))))
8.0ms
(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)))

series188.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
61.0ms
(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)))
34.0ms
(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

prune346.0ms

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: 12.4b

Counts
98 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
28.1b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
28.1b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
28.1b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
21×unpow-prod-down
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod div-inv sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 72
Calls
4 calls:
2.0ms
(sqrt (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
4.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
4.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
4.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

series451.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
118.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
118.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
122.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
04371482
112421406
250021406

prune490.0ms

Filtered
75 candidates to 84 candidates (-12.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New84084
Fresh077
Picked011
Done022
Total841094

Merged error: 12.4b

Counts
94 → 10

regimes636.0ms

Accuracy

91.8% (0.4b remaining)

Error of 12.9b against oracle of 12.4b and baseline of 17.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04950
14950

end0.0ms

sample5.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results
1.3s1523×body1280valid
714.0ms1246×body640valid
711.0ms4270×body80valid
267.0ms635×body320valid
90.0ms328×body160valid

Profiling

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