Details

Time bar (total: 10.5s)

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

sample201.0ms

Algorithm
intervals
Results
134.0ms123×body1280valid
43.0ms68×body640valid
7.0ms16×body320valid
5.0ms40×body80valid
3.0ms9×body160valid

simplify107.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (98.0ms)

IterNodesCost
0517126

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.7b

Counts
2 → 1

localize14.0ms

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 kx) 2)
0.2b
(pow.f64 (sin.f64 ky) 2)
4.3b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite35.0ms

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:
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))
3.0ms
(pow.f64 (sin.f64 kx) 2)
3.0ms
(pow.f64 (sin.f64 ky) 2)
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(*.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 kx) 2)
16.0ms
(pow.f64 (sin.f64 ky) 2)
89.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify92.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049682288
149682288

prune142.0ms

Filtered
75 candidates to 115 candidates (-53.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10411115
Fresh000
Picked101
Done000
Total10511116

Merged error: 3.0b

Counts
116 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (sin.f64 kx) 2)
0.2b
(/.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 ky) 2)
4.3b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity_binary64
27×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
25×sqrt-prod_binary64
24×times-frac_binary64
16×unpow-prod-down_binary64
10×distribute-lft-out_binary64
8×associate-/r*_binary64 add-exp-log_binary64
7×pow1_binary64
6×pow-unpow_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64 sqrt-div_binary64
3×associate-/l*_binary64
2×pow-to-exp_binary64 flip3-+_binary64 unpow2_binary64 pow-pow_binary64 sqr-pow_binary64 associate-/r/_binary64 flip-+_binary64 pow-exp_binary64
1×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 → 102
Calls
4 calls:
3.0ms
(pow.f64 (sin.f64 kx) 2)
12.0ms
(/.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 ky) 2)
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(pow.f64 (sin.f64 kx) 2)
193.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
14.0ms
(pow.f64 (sin.f64 ky) 2)
92.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify88.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
051932324

prune98.0ms

Filtered
67 candidates to 114 candidates (-70.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1131114
Fresh01010
Picked011
Done000
Total11312125

Merged error: 3.0b

Counts
125 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 ky) (sin.f64 th))
0.2b
(pow.f64 (sin.f64 ky) 2)
1.5b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.3b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity_binary64
16×add-sqr-sqrt_binary64
15×sqrt-prod_binary64
13×add-cube-cbrt_binary64
12×add-exp-log_binary64
11×add-cbrt-cube_binary64
9×unpow-prod-down_binary64
8×associate-/r*_binary64 pow1_binary64 times-frac_binary64
6×distribute-lft-out_binary64
4×add-log-exp_binary64 sqrt-div_binary64
3×pow-unpow_binary64 associate-*r*_binary64 associate-*l*_binary64
2×flip3-+_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-/r/_binary64 prod-exp_binary64 sin-mult_binary64 div-exp_binary64 flip-+_binary64
1×pow-to-exp_binary64 pow-prod-down_binary64 associate-/l/_binary64 pow1/2_binary64 unpow2_binary64 pow-pow_binary64 sqr-pow_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 pow-exp_binary64 *-commutative_binary64
Counts
4 → 88
Calls
4 calls:
5.0ms
(*.f64 (sin.f64 ky) (sin.f64 th))
3.0ms
(pow.f64 (sin.f64 ky) 2)
14.0ms
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(*.f64 (sin.f64 ky) (sin.f64 th))
15.0ms
(pow.f64 (sin.f64 ky) 2)
208.0ms
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
91.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify99.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049871830
149871830

prune87.0ms

Filtered
61 candidates to 100 candidates (-63.9%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1000100
Fresh01010
Picked011
Done011
Total10012112

Merged error: 3.0b

Counts
112 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (sin.f64 ky) 2)
0.4b
(*.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)))))
4.8b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.8b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite38.0ms

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
9×unpow-prod-down_binary64
7×pow1_binary64 add-exp-log_binary64
6×cbrt-div_binary64 distribute-lft-out_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64
3×flip3-+_binary64 pow-unpow_binary64 associate-*l*_binary64 unswap-sqr_binary64 flip-+_binary64
2×associate-*r/_binary64 pow1/3_binary64 sqrt-div_binary64
1×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:
3.0ms
(pow.f64 (sin.f64 ky) 2)
15.0ms
(*.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)))))
8.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow.f64 (sin.f64 ky) 2)
195.0ms
(*.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)))))
136.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
143.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify92.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
050512396

prune116.0ms

Filtered
62 candidates to 90 candidates (-45.2%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New90090
Fresh099
Picked011
Done022
Total9012102

Merged error: 3.0b

Counts
102 → 12

regimes308.0ms

Accuracy

71.1% (0.4b remaining)

Error of 3.1b against oracle of 2.6b and baseline of 4.1b

bsearch2.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06584
16584

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.9s3698×body1280valid
1.4s2073×body640valid
309.0ms684×body320valid
163.0ms1221×body80valid
88.0ms324×body160valid

Profiling

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