Details

Time bar (total: 6.4s)

sample97.0ms

Algorithm
intervals
Results
32.0ms50×body1280valid
23.0ms38×body640valid
13.0ms141×body80valid
6.0ms18×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

prune6.0ms

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: 15.7b

Counts
2 → 1

localize17.0ms

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)
6.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.8b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite37.0ms

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)))
17.0ms
(* (* (* -2.0 J) (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:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
30.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
36.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
41.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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

prune420.0ms

Filtered
97 candidates to 62 candidates (36.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New89897
Fresh000
Picked101
Done000
Total90898

Merged error: 11.2b

Counts
98 → 8

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)
6.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.9b
(* (* -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
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)
6.0ms
(sqrt (+ 1.0 (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)))))

series117.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
31.0ms
(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)))
45.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0488987
12021866
25002866

prune555.0ms

Filtered
94 candidates to 59 candidates (37.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh077
Picked011
Done000
Total948102

Merged error: 11.2b

Counts
102 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
6.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.8b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.8b
(sqrt (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 (+ 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)))
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))))

series186.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(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)))
58.0ms
(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))))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune307.0ms

Filtered
88 candidates to 62 candidates (29.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh066
Picked011
Done011
Total87996

Merged error: 11.2b

Counts
96 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×*-un-lft-identity
12×pow1 cbrt-prod
9×sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt add-cube-cbrt
4×add-exp-log frac-times add-cbrt-cube add-log-exp
3×distribute-lft-out
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 69
Calls
4 calls:
15.0ms
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (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)))
6.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
59.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
58.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
60.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify97.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
02101284
15641214
225731208
350011182

prune549.0ms

Filtered
81 candidates to 63 candidates (22.2%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New81081
Fresh066
Picked011
Done022
Total81990

Merged error: 11.2b

Counts
90 → 9

regimes617.0ms

Accuracy

92.2% (0.4b remaining)

Error of 13.2b against oracle of 12.8b and baseline of 18.3b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04950
14950

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.0s1554×body1280valid
579.0ms1245×body640valid
396.0ms4251×body80valid
216.0ms634×body320valid
69.0ms319×body160valid

Profiling

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