Details

Time bar (total: 2.4s)

analyze1.2s (50.6%)

Algorithm
1×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)

sample207.0ms (8.4%)

Algorithm
1×intervals
Results
145.0ms132×body1280valid
35.0ms54×body640valid
7.0ms15×body320valid
5.0ms45×body80valid
3.0ms10×body160valid
Compiler

Compiled 33 to 32 computations (3% saved)

simplify111.0ms (4.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
0511626

prune10.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.0b

Counts
2 → 1
Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (0.6%)

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)))

rewrite34.0ms (1.4%)

Algorithm
1×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:

17.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
8.0ms
(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)

series83.0ms (3.4%)

Counts
4 → 12
Calls

4 calls:

54.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
21.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms
(pow.f64 (sin.f64 kx) 2)
4.0ms
(pow.f64 (sin.f64 ky) 2)

simplify118.0ms (4.8%)

Algorithm
1×egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049632288
149632288

prune150.0ms (6.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10411115
Fresh000
Picked101
Done000
Total10511116

Merged error: 1.6b

Counts
116 → 11
Compiler

Compiled 3026 to 1703 computations (43.7% saved)

localize19.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.5b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.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)))

rewrite75.0ms (3.1%)

Algorithm
1×rewrite-expression-head
Rules
101×sqrt-prod_binary64
87×*-un-lft-identity_binary64
66×times-frac_binary64
53×add-sqr-sqrt_binary64
51×add-cube-cbrt_binary64
45×add-exp-log_binary64
39×associate-*l*_binary64
27×add-cbrt-cube_binary64
20×prod-exp_binary64
18×distribute-lft-out_binary64 unpow-prod-down_binary64
12×sqrt-div_binary64
11×associate-/r*_binary64 pow1_binary64 div-exp_binary64
10×cbrt-unprod_binary64
6×cbrt-undiv_binary64
4×flip3-+_binary64 add-log-exp_binary64 associate-/r/_binary64 flip-+_binary64
3×pow-prod-down_binary64 1-exp_binary64 associate-*r/_binary64 rec-exp_binary64 associate-/l*_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 div-inv_binary64
1×associate-*r*_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 166
Calls

4 calls:

37.0ms
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
14.0ms
(/.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)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series154.0ms (6.3%)

Counts
4 → 12
Calls

4 calls:

60.0ms
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
52.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
21.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify153.0ms (6.3%)

Algorithm
1×egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
049495592
149495592

prune81.0ms (3.3%)

Profiling

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