Details

Time bar (total: 9.9s)

sample213.0ms

Algorithm
intervals
Results
138.0ms126×body1280valid
40.0ms59×body640valid
9.0ms20×body320valid
5.0ms42×body80valid
3.0ms9×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0476616
1476616

prune19.0ms

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: 3.4b

Counts
2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

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:
17.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series115.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
23.0ms
(pow (sin kx) 2.0)
20.0ms
(pow (sin ky) 2.0)
21.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify64.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049481475
149481475

prune293.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10310113
Fresh011
Picked101
Done000
Total10411115

Merged error: 2.3b

Counts
115 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sin ky) (pow (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1/2)) (sin th))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.2b
(pow (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1/2)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
37×add-sqr-sqrt
35×unpow-prod-down
31×associate-*l*
30×times-frac
27×add-cube-cbrt
17×add-exp-log
9×pow1 pow-unpow add-cbrt-cube
8×distribute-lft-out
7×sqr-pow
4×pow-to-exp pow-exp prod-exp add-log-exp unswap-sqr
3×pow-pow div-exp associate-*r*
2×cbrt-unprod
1×cbrt-undiv pow-prod-down associate-*l/ *-commutative div-inv unpow1/2
Counts
4 → 108
Calls
4 calls:
20.0ms
(* (/ (sin ky) (pow (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1/2)) (sin th))
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
9.0ms
(pow (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1/2)

series126.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (/ (sin ky) (pow (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1/2)) (sin th))
20.0ms
(pow (sin kx) 2.0)
20.0ms
(pow (sin ky) 2.0)
32.0ms
(pow (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1/2)

simplify38.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
052591581

prune270.0ms

Filtered
81 candidates to 120 candidates (-48.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1191120
Fresh1910
Picked011
Done000
Total12011131

Merged error: 2.3b

Counts
131 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite49.0ms

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:
3.0ms
(pow (sin ky) 2.0)
21.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
12.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series139.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(pow (sin ky) 2.0)
53.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
45.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
051072217

prune290.0ms

Filtered
86 candidates to 145 candidates (-68.6%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh099
Picked011
Done011
Total14511156

Merged error: 2.3b

Counts
156 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.7b
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
87×*-un-lft-identity
66×times-frac
53×add-sqr-sqrt
51×add-cube-cbrt
45×add-exp-log
39×associate-*l*
27×add-cbrt-cube
20×prod-exp
18×unpow-prod-down distribute-lft-out
12×sqrt-div
11×pow1 div-exp associate-/r*
10×cbrt-unprod
6×cbrt-undiv
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×rec-exp 1-exp associate-*r/ pow-prod-down associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×frac-times frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 166
Calls
4 calls:
16.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
34.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
55.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
21.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
056103426

prune448.0ms

Filtered
105 candidates to 178 candidates (-69.5%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1771178
Fresh178
Picked011
Done022
Total17811189

Merged error: 2.3b

Counts
189 → 11

regimes903.0ms

Accuracy

0% (1.3b remaining)

Error of 3.8b against oracle of 2.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01617
11617

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.1s3817×body1280valid
1.4s2008×body640valid
337.0ms684×body320valid
177.0ms1219×body80valid
85.0ms272×body160valid

Profiling

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