Details

Time bar (total: 8.0s)

analyze2.0s

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
49.0ms53×body1280valid
20.0ms36×body640valid
15.0ms135×body80valid
8.0ms20×body320valid
3.0ms12×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0550124

prune13.0ms

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: 14.4b

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)
4.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite45.0ms

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:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
11.0ms
(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)))
14.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series186.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
41.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
59.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
79.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify75.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
049831601
149831601

prune280.0ms

Filtered
67 candidates to 97 candidates (-44.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New871097
Fresh011
Picked101
Done000
Total881199

Merged error: 11.0b

Counts
99 → 11

localize16.0ms

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)
4.9b
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
8.7b
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

rewrite33.0ms

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)
7.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
12.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

series114.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* J (* 2.0 (cos (/ K 2.0))))
31.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
32.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
43.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049861398
149861398

prune235.0ms

Filtered
60 candidates to 90 candidates (-50.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New84690
Fresh5510
Picked011
Done000
Total8912101

Merged error: 11.0b

Counts
101 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 0.5 (cos (* K 0.5))) J)
0.2b
(pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)
4.9b
(sqrt (+ 1.0 (pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)))
8.7b
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
51×*-un-lft-identity
50×add-sqr-sqrt
49×add-cube-cbrt
24×add-exp-log
14×add-cbrt-cube
13×pow1 associate-/l*
6×div-exp prod-exp
5×div-inv
4×sqrt-div associate-*r/ pow-prod-down pow-exp sqrt-prod add-log-exp
3×cbrt-undiv pow-unpow associate-*l* associate-/r* cbrt-unprod
2×pow-pow flip3-+ flip-+
1×pow-to-exp unpow-prod-down rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r* clear-num *-commutative associate-/l/ distribute-lft-out sqr-pow
Counts
4 → 125
Calls
4 calls:
6.0ms
(/ (/ 0.5 (cos (* K 0.5))) J)
9.0ms
(pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)
4.0ms
(sqrt (+ 1.0 (pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)))
9.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)))))

series116.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ (/ 0.5 (cos (* K 0.5))) J)
31.0ms
(pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)
31.0ms
(sqrt (+ 1.0 (pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)))
44.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (* U (/ (/ 0.5 (cos (* K 0.5))) J)) 2.0)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
052142226

prune396.0ms

Filtered
106 candidates to 137 candidates (-29.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1370137
Fresh01010
Picked011
Done011
Total13712149

Merged error: 11.0b

Counts
149 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
4.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.6b
(* (* (* -2.0 (* J (* (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))))

rewrite35.0ms

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)))
9.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
22.0ms
(* (* (* -2.0 (* J (* (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))))

series113.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(cbrt (cos (/ K 2.0)))
20.0ms
(cbrt (cos (/ K 2.0)))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
42.0ms
(* (* (* -2.0 (* J (* (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))))

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
051701358

prune224.0ms

Filtered
54 candidates to 83 candidates (-53.7%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New79483
Fresh189
Picked101
Done022
Total811495

Merged error: 11.0b

Counts
95 → 14

regimes562.0ms

Accuracy

0% (5.4b remaining)

Error of 18.0b against oracle of 12.6b and baseline of 18.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02324
12324

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.3s1526×body1280valid
726.0ms1232×body640valid
500.0ms4297×body80valid
255.0ms620×body320valid
89.0ms325×body160valid
1.0ms1×body1280invalid
0.0ms3×body80invalid

Profiling

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