Details

Time bar (total: 9.6s)

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14

sample108.0ms

Algorithm
intervals
Results
47.0ms56×body1280valid
24.0ms41×body640valid
16.0ms135×body80valid
7.0ms16×body320valid
2.0ms8×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0550124

prune17.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.9b

Counts
2 → 2

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)
9.0b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(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)))
6.0ms
(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)))

series114.0ms

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)
41.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

simplify59.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049641603
149641603

prune246.0ms

Filtered
69 candidates to 97 candidates (-40.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New91697
Fresh011
Picked011
Done000
Total91899

Merged error: 15.1b

Counts
99 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* J (* 2.0 (cos (/ K 2.0))))
0.2b
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
9.0b
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
16×pow1
14×add-cbrt-cube
12×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt
9×prod-exp
7×unpow-prod-down
6×associate-*l* pow-prod-down cbrt-unprod
4×sqrt-div associate-*r/ pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 78
Calls
4 calls:
5.0ms
(* J (* 2.0 (cos (/ K 2.0))))
7.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
11.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* J (* 2.0 (cos (/ K 2.0))))
32.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
40.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
35.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050501401

prune212.0ms

Filtered
61 candidates to 90 candidates (-47.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New87390
Fresh066
Picked011
Done011
Total871198

Merged error: 15.1b

Counts
98 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (cos (/ K 2.0)))
0.4b
(cbrt (cos (/ K 2.0)))
9.0b
(* (* (* J (* -2.0 (* (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))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-exp-log
18×add-cbrt-cube
15×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 → 71
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
19.0ms
(* (* (* J (* -2.0 (* (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))))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series111.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(cbrt (cos (/ K 2.0)))
17.0ms
(cbrt (cos (/ K 2.0)))
44.0ms
(* (* (* J (* -2.0 (* (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))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049801358
149801358

prune248.0ms

Filtered
55 candidates to 83 candidates (-50.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New80383
Fresh358
Picked101
Done022
Total841094

Merged error: 15.1b

Counts
94 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (cos (/ K 2.0)))
0.4b
(cbrt (cos (/ K 2.0)))
9.0b
(* (* (* J (* -2.0 (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (log (exp (cbrt (cos (/ K 2.0)))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-exp-log
22×add-cbrt-cube
15×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 → 71
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
21.0ms
(* (* (* J (* -2.0 (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (log (exp (cbrt (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)))

series109.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(cbrt (cos (/ K 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))
41.0ms
(* (* (* J (* -2.0 (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (log (exp (cbrt (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)))

simplify42.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050961358

prune234.0ms

Filtered
55 candidates to 83 candidates (-50.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh077
Picked101
Done022
Total831093

Merged error: 15.1b

Counts
93 → 10

regimes546.0ms

Accuracy

84.8% (0.8b remaining)

Error of 13.3b against oracle of 12.5b and baseline of 17.8b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
048118
148118

end0.0ms

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14

sample3.2s

Algorithm
intervals
Results
1.4s1547×body1280valid
756.0ms1260×body640valid
525.0ms4272×body80valid
259.0ms613×body320valid
85.0ms308×body160valid
0.0ms2×body80invalid

Profiling

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