Details

Time bar (total: 5.0s)

analyze1.3s

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

sample221.0ms

Algorithm
intervals
Results
150.0ms132×body1280valid
37.0ms54×body640valid
7.0ms15×body320valid
6.0ms45×body80valid
3.0ms10×body160valid

simplify107.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (98.0ms)

IterNodesCost
0501126

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.0b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b
(pow.f64 (sin.f64 ky) 2)
0.2b
(pow.f64 (sin.f64 kx) 2)
2.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity_binary64
34×add-sqr-sqrt_binary64
30×associate-*l*_binary64
26×times-frac_binary64
25×add-cube-cbrt_binary64
21×sqrt-prod_binary64
14×unpow-prod-down_binary64
11×add-exp-log_binary64
9×pow1_binary64 add-cbrt-cube_binary64
8×distribute-lft-out_binary64
6×pow-unpow_binary64
4×add-log-exp_binary64 sqrt-div_binary64
3×associate-*r*_binary64 unswap-sqr_binary64
2×pow-to-exp_binary64 flip3-+_binary64 cbrt-unprod_binary64 unpow2_binary64 pow-pow_binary64 sqr-pow_binary64 associate-/r/_binary64 prod-exp_binary64 flip-+_binary64 pow-exp_binary64
1×pow-prod-down_binary64 pow1/2_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 div-inv_binary64 div-exp_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 103
Calls
4 calls:
18.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
3.0ms
(pow.f64 (sin.f64 ky) 2)
3.0ms
(pow.f64 (sin.f64 kx) 2)
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
15.0ms
(pow.f64 (sin.f64 ky) 2)
15.0ms
(pow.f64 (sin.f64 kx) 2)
97.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify87.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049712288
149712288

prune706.0ms

Filtered
77 candidates to 115 candidates (-49.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10411115
Fresh000
Picked101
Done000
Total10511116

Merged error: 1.6b

Counts
116 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.2b
(pow.f64 (sin.f64 kx) 2)
0.3b
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity_binary64
50×times-frac_binary64
49×add-sqr-sqrt_binary64
41×sqrt-prod_binary64
40×add-cube-cbrt_binary64
30×associate-*r*_binary64
19×unpow-prod-down_binary64
16×distribute-lft-out_binary64
12×add-exp-log_binary64
11×add-cbrt-cube_binary64
8×associate-/r*_binary64 pow1_binary64
6×sqrt-div_binary64
4×add-log-exp_binary64 associate-/r/_binary64
3×flip3-+_binary64 pow-unpow_binary64 associate-*l*_binary64 unswap-sqr_binary64 associate-/l*_binary64 flip-+_binary64
2×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64
1×pow-to-exp_binary64 pow-prod-down_binary64 pow1/2_binary64 unpow2_binary64 associate-*r/_binary64 pow-pow_binary64 sqr-pow_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 pow-exp_binary64 *-commutative_binary64
Counts
4 → 134
Calls
4 calls:
19.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms
(pow.f64 (sin.f64 kx) 2)
15.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
18.0ms
(pow.f64 (sin.f64 kx) 2)
203.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
97.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify118.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
050223544

prune509.0ms

Filtered
83 candidates to 146 candidates (-75.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1442146
Fresh3710
Picked011
Done000
Total14710157

Merged error: 1.6b

Counts
157 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
2.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
114×sqrt-prod_binary64
94×*-un-lft-identity_binary64
66×times-frac_binary64
56×add-sqr-sqrt_binary64
54×add-cube-cbrt_binary64
22×associate-/r*_binary64
20×distribute-lft-out_binary64 unpow-prod-down_binary64
12×sqrt-div_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
6×pow1_binary64 associate-/l*_binary64
4×flip3-+_binary64 add-log-exp_binary64 associate-/r/_binary64 flip-+_binary64
2×pow1/2_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 156
Calls
4 calls:
15.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
19.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series647.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
220.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
92.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
96.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify108.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049955213
149955213

prune84.0ms

Filtered
94 candidates to 168 candidates (-78.7%)

Profiling

Loading profile data...