Details

Time bar (total: 13.0s)

analyze1.2s (9.3%)

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
Compiler

Compiled 17 to 15 computations (11.8% saved)

sample160.0ms (1.2%)

Algorithm
intervals
Results
114.0ms142×body1024valid
23.0ms50×body512valid
6.0ms44×body128valid
6.0ms20×body256valid
Compiler

Compiled 33 to 32 computations (3% saved)

simplify87.0ms (0.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
0516926

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.3b

Counts
2 → 1
Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (0.1%)

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)
0.3b
(pow.f64 (sin.f64 kx) 2)
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite47.0ms (0.4%)

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
pow1_binary64 add-cbrt-cube_binary64
distribute-lft-out_binary64
pow-unpow_binary64
add-log-exp_binary64 sqrt-div_binary64
associate-*r*_binary64 unswap-sqr_binary64
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
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:

21.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(pow.f64 (sin.f64 kx) 2)
3.0ms
(pow.f64 (sin.f64 ky) 2)

series628.0ms (4.8%)

Counts
4 → 12
Calls

4 calls:

406.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
172.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms
(pow.f64 (sin.f64 ky) 2)
25.0ms
(pow.f64 (sin.f64 kx) 2)

simplify74.0ms (0.6%)

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050122288

prune843.0ms (6.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New10312115
Fresh000
Picked011
Done000
Total10313116

Merged error: 2.3b

Counts
116 → 13
Compiler

Compiled 14271 to 10562 computations (26% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (sin.f64 kx) 2)
0.5b
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite82.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
104×sqrt-prod_binary64
60×add-sqr-sqrt_binary64
50×*-un-lft-identity_binary64
34×sqrt-pow1_binary64
30×pow1_binary64
28×sqrt-div_binary64
20×add-cube-cbrt_binary64
19×swap-sqr_binary64
18×pow1/2_binary64
15×unpow-prod-down_binary64
14×distribute-lft-out_binary64
11×associate-*r*_binary64 associate-*l*_binary64
10×rem-sqrt-square_binary64
pow-prod-up_binary64 unswap-sqr_binary64
flip3-+_binary64 flip-+_binary64
add-exp-log_binary64
add-cbrt-cube_binary64
pow-prod-down_binary64 pow-sqr_binary64
add-log-exp_binary64 sqr-abs_binary64 frac-times_binary64
pow-unpow_binary64
associate-*r/_binary64 associate-*l/_binary64
pow-to-exp_binary64 cbrt-unprod_binary64 unpow2_binary64 rem-square-sqrt_binary64 pow-pow_binary64 sqr-pow_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 pow-exp_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 147
Calls

4 calls:

33.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(pow.f64 (sin.f64 kx) 2)

series495.0ms (3.8%)

Counts
4 → 12
Calls

4 calls:

176.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
148.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
145.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.0ms
(pow.f64 (sin.f64 kx) 2)

simplify101.0ms (0.8%)

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
049423097
149423097

prune291.0ms (2.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1590159
Fresh01111
Picked011
Done011
Total15913172

Merged error: 2.3b

Counts
172 → 13
Compiler

Compiled 5374 to 3340 computations (37.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite134.0ms (1%)

Algorithm
rewrite-expression-head
Rules
168×cbrt-prod_binary64
157×*-un-lft-identity_binary64
142×add-sqr-sqrt_binary64
136×times-frac_binary64
101×sqrt-prod_binary64
79×add-cube-cbrt_binary64
45×swap-sqr_binary64
36×distribute-lft-out_binary64
33×associate-*r*_binary64 associate-*l*_binary64
30×unpow-prod-down_binary64
16×unswap-sqr_binary64
14×pow1_binary64 sqrt-div_binary64
associate-/r/_binary64
flip3-+_binary64 flip-+_binary64
pow1/3_binary64 add-exp-log_binary64
cbrt-div_binary64 add-log-exp_binary64 add-cbrt-cube_binary64 div-inv_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
cbrt-unprod_binary64 associate-*r/_binary64 pow-plus_binary64 prod-exp_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 199
Calls

4 calls:

60.0ms
(*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series933.0ms (7.2%)

Counts
4 → 12
Calls

4 calls:

448.0ms
(*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
169.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
163.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
153.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify149.0ms (1.1%)

Algorithm
egg-herbie
Counts
211 → 211
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0506610008

prune779.0ms (6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New2110211
Fresh01010
Picked011
Done022
Total21113224

Merged error: 2.3b

Counts
224 → 13
Compiler

Compiled 12750 to 7435 computations (41.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (sin.f64 kx) 2)
0.3b
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.5b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.5b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite50.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
18×add-sqr-sqrt_binary64
16×cbrt-prod_binary64
12×add-cube-cbrt_binary64
11×associate-*r*_binary64
10×sqrt-prod_binary64
unpow-prod-down_binary64
pow1_binary64 add-exp-log_binary64
cbrt-div_binary64 distribute-lft-out_binary64 add-cbrt-cube_binary64
add-log-exp_binary64
flip3-+_binary64 pow-unpow_binary64 associate-*l*_binary64 unswap-sqr_binary64 flip-+_binary64
associate-*r/_binary64 pow1/3_binary64 sqrt-div_binary64
pow-to-exp_binary64 pow-prod-down_binary64 cbrt-unprod_binary64 unpow2_binary64 pow-pow_binary64 sqr-pow_binary64 prod-exp_binary64 pow-exp_binary64 *-commutative_binary64
Counts
4 → 78
Calls

4 calls:

18.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(pow.f64 (sin.f64 kx) 2)

series738.0ms (5.7%)

Counts
4 → 12
Calls

4 calls:

286.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
216.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
211.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms
(pow.f64 (sin.f64 kx) 2)

simplify81.0ms (0.6%)

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049332396
149332396

prune304.0ms (2.3%)

Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New90090
Fresh099
Picked011
Done033
Total9013103

Merged error: 2.3b

Counts
103 → 13
Compiler

Compiled 3316 to 2046 computations (38.3% saved)

regimes301.0ms (2.3%)

Compiler

Compiled 3063 to 2473 computations (19.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01626
11626

end0.0ms (0%)

sample5.4s (41.8%)

Algorithm
intervals
Results
3.8s4672×body1024valid
682.0ms1390×body512valid
195.0ms1437×body128valid
144.0ms493×body256valid
15.0msbody2048valid
Compiler

Compiled 364 to 295 computations (19% saved)

Profiling

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