Details

Time bar (total: 11.0s)

analyze1.4s

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
25%74.9%0.1%8
54.6%45.2%0.1%9
56.2%43.7%0.1%10
62.4%37.4%0.1%11
65.9%33.9%0.1%12
66.3%33.5%0.1%13
69%30.8%0.1%14

sample185.0ms

Algorithm
intervals
Results
105.0ms100×body1280valid
43.0ms68×body640valid
12.0ms27×body320valid
9.0ms49×body80valid
3.0ms12×body160valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
0476616
1476616

prune20.0ms

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: 2.7b

Counts
2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b
(pow (sin kx) 2.0)
0.2b
(pow (sin ky) 2.0)
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
34×add-sqr-sqrt
30×associate-*l*
26×times-frac
25×add-cube-cbrt
21×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×pow1 add-cbrt-cube
8×distribute-lft-out
6×pow-unpow
4×sqrt-div add-log-exp
3×associate-*r* unswap-sqr
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
16.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series110.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms
(pow (sin kx) 2.0)
24.0ms
(pow (sin ky) 2.0)
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
052281477

prune281.0ms

Filtered
77 candidates to 113 candidates (-46.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10013113
Fresh011
Picked101
Done000
Total10114115

Merged error: 2.2b

Counts
115 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
41×sqrt-prod
40×add-cube-cbrt
30×associate-*r*
19×unpow-prod-down
16×distribute-lft-out
12×add-exp-log
11×add-cbrt-cube
8×pow1 associate-/r*
6×sqrt-div
4×associate-/r/ add-log-exp
3×pow-unpow flip3-+ associate-*l* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down pow-exp clear-num *-commutative sqr-pow
Counts
4 → 133
Calls
4 calls:
2.0ms
(pow (sin ky) 2.0)
12.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
17.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series128.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(pow (sin ky) 2.0)
41.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
45.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049332217
149332217

prune273.0ms

Filtered
85 candidates to 145 candidates (-70.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1414145
Fresh6713
Picked101
Done000
Total14811159

Merged error: 2.2b

Counts
159 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
0.3b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
0.3b
(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
370×times-frac
293×*-un-lft-identity
208×add-sqr-sqrt
186×add-cube-cbrt
132×sqrt-prod
89×associate-*r*
52×unpow-prod-down distribute-lft-out
36×add-exp-log
31×associate-/r*
20×add-cbrt-cube
15×div-exp
11×associate-/l*
10×div-inv
8×pow1
7×cbrt-undiv prod-exp unswap-sqr
4×rec-exp sqrt-div 1-exp add-log-exp
3×associate-*l* cbrt-unprod
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ associate-/l/
1×rem-sqrt-square pow-flip sqrt-pow1 pow1/2 associate-*r/ pow-prod-down un-div-inv *-commutative inv-pow
Counts
4 → 322
Calls
4 calls:
13.0ms
(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
14.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
31.0ms
(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series145.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
41.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
48.0ms
(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify88.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049576414
149576414

prune552.0ms

Filtered
162 candidates to 334 candidates (-106.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3322334
Fresh01010
Picked101
Done000
Total33312345

Merged error: 2.2b

Counts
345 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.5b
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
100×sqrt-prod
52×add-sqr-sqrt
50×*-un-lft-identity
34×sqrt-pow1
30×pow1
28×sqrt-div
20×add-cube-cbrt
19×swap-sqr
18×pow1/2
15×unpow-prod-down
14×distribute-lft-out
11×associate-*r* associate-*l*
9×pow-prod-up unswap-sqr
8×flip3-+ flip-+
7×add-exp-log
6×add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times add-log-exp
3×pow-unpow
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 pow-to-exp pow-pow pow-plus sqrt-unprod pow-exp prod-exp rem-square-sqrt *-commutative cbrt-unprod sqr-pow
Counts
4 → 142
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
24.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin ky) 2.0)
21.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049322020
149322020

prune238.0ms

Filtered
73 candidates to 154 candidates (-111.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1540154
Fresh01111
Picked011
Done000
Total15412166

Merged error: 2.2b

Counts
166 → 12

regimes895.0ms

Accuracy

0% (1.6b remaining)

Error of 4.3b against oracle of 2.6b and baseline of 4.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01729
11729

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.9s3670×body1280valid
1.3s2018×body640valid
339.0ms740×body320valid
165.0ms1278×body80valid
101.0ms294×body160valid

Profiling

Loading profile data...