Details

Time bar (total: 15.5s)

analyze1.2s (8%)

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)

sample149.0ms (1%)

Algorithm
intervals
Results
96.0ms133×body1024valid
27.0ms60×body512valid
7.0ms25×body256valid
4.0ms37×body128valid
1.0msbody2048valid
Compiler

Compiled 33 to 32 computations (3% saved)

simplify169.0ms (1.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
0517026

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
2.7b
Counts
2 → 1
Compiler

Compiled 32 to 28 computations (12.5% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(pow.f64 (sin.f64 kx) 2)
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))
0.1b
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
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)
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite42.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity_binary64_78
34×add-sqr-sqrt_binary64_100
30×associate-*l*_binary64_19
26×times-frac_binary64_84
25×add-cube-cbrt_binary64_113
21×sqrt-prod_binary64_94
14×unpow-prod-down_binary64_157
11×add-exp-log_binary64_116
add-cbrt-cube_binary64_114 pow1_binary64_139
distribute-lft-out_binary64_29
pow-unpow_binary64_155
add-log-exp_binary64_117 sqrt-div_binary64_95
associate-*r*_binary64_18 unswap-sqr_binary64_46
pow-exp_binary64_146 pow-to-exp_binary64_147 cbrt-unprod_binary64_111 prod-exp_binary64_127 flip-+_binary64_52 unpow2_binary64_143 sqr-pow_binary64_50 pow-pow_binary64_150 associate-/r/_binary64_24 flip3-+_binary64_81
*-commutative_binary64_9 sqrt-pow1_binary64_96 cbrt-undiv_binary64_112 div-exp_binary64_129 rem-sqrt-square_binary64_91 div-inv_binary64_75 associate-*l/_binary64_21 pow-prod-down_binary64_149 pow1/2_binary64_158
Counts
4 → 103
Calls

8 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))
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)
0.0ms
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series940.0ms (6%)

Counts
4 → 39
Calls

4 calls:

689.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
193.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms
(pow.f64 (sin.f64 ky) 2)
27.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 1385 to 1117 computations (19.4% saved)

simplify73.0ms (0.5%)

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049933140
149933140

prune310.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New12913142
Fresh000
Picked101
Done000
Total13013143
Error
1.1b
Counts
143 → 13
Compiler

Compiled 3742 to 2092 computations (44.1% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.1b
(sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.2b
(pow.f64 (sin.f64 ky) 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)))))
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite67.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
104×sqrt-prod_binary64_94
60×add-sqr-sqrt_binary64_100
50×*-un-lft-identity_binary64_78
34×sqrt-pow1_binary64_96
30×pow1_binary64_139
28×sqrt-div_binary64_95
20×add-cube-cbrt_binary64_113
19×swap-sqr_binary64_45
18×pow1/2_binary64_158
15×unpow-prod-down_binary64_157
14×distribute-lft-out_binary64_29
11×associate-*l*_binary64_19 associate-*r*_binary64_18
10×rem-sqrt-square_binary64_91
pow-prod-up_binary64_148 unswap-sqr_binary64_46
flip-+_binary64_52 flip3-+_binary64_81
add-exp-log_binary64_116
add-cbrt-cube_binary64_114
pow-sqr_binary64_51 pow-prod-down_binary64_149
sqr-abs_binary64_93 add-log-exp_binary64_117 frac-times_binary64_88
pow-unpow_binary64_155
associate-*l/_binary64_21 associate-*r/_binary64_20
pow2_binary64_159 *-commutative_binary64_9 pow-exp_binary64_146 pow-to-exp_binary64_147 cbrt-unprod_binary64_111 prod-exp_binary64_127 unpow2_binary64_143 sqr-pow_binary64_50 sqrt-unprod_binary64_98 pow-pow_binary64_150 rem-square-sqrt_binary64_90 pow-plus_binary64_141
Counts
4 → 147
Calls

8 calls:

27.0ms
(*.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)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(pow.f64 (sin.f64 ky) 2)
0.0ms
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series623.0ms (4%)

Counts
4 → 39
Calls

4 calls:

199.0ms
(*.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)))))
198.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
193.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
33.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 1844 to 1434 computations (22.2% saved)

simplify102.0ms (0.7%)

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049793823
149793823

prune329.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1860186
Fresh01212
Picked011
Done000
Total18613199
Error
1.1b
Counts
199 → 13
Compiler

Compiled 5953 to 3558 computations (40.2% saved)

localize22.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.4b
(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite52.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity_binary64_78
30×sqrt-prod_binary64_94 cbrt-prod_binary64_109
25×add-sqr-sqrt_binary64_100
24×times-frac_binary64_84
22×add-cube-cbrt_binary64_113
12×unpow-prod-down_binary64_157 distribute-lft-out_binary64_29
sqrt-div_binary64_95
pow1_binary64_139
add-cbrt-cube_binary64_114 add-log-exp_binary64_117 flip-+_binary64_52 add-exp-log_binary64_116 flip3-+_binary64_81
sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 pow1/2_binary64_158
associate-/r/_binary64_24
cbrt-div_binary64_110 pow1/3_binary64_160 div-inv_binary64_75
Counts
4 → 90
Calls

8 calls:

11.0ms
(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)))
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)))
0.0ms
(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series1.3s (8.4%)

Counts
4 → 42
Calls

4 calls:

705.0ms
(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
211.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
196.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
196.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Compiler

Compiled 3408 to 2402 computations (29.5% saved)

simplify79.0ms (0.5%)

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052183689

prune384.0ms (2.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh01111
Picked011
Done011
Total13213145
Error
1.1b
Counts
145 → 13
Compiler

Compiled 7539 to 4445 computations (41% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))) (sin.f64 th))
0.1b
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2)))))
0.1b
(+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2)))
0.6b
(cbrt.f64 (sin.f64 ky))
0.6b
(cbrt.f64 (sin.f64 ky))
0.7b
(pow.f64 (cbrt.f64 (sin.f64 ky)) 4)
2.5b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64_100
10×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
cbrt-prod_binary64_109
unpow-prod-down_binary64_157 pow1_binary64_139
add-exp-log_binary64_116
add-cbrt-cube_binary64_114 add-log-exp_binary64_117
sqrt-prod_binary64_94 pow1/3_binary64_160 pow-unpow_binary64_155
pow-pow_binary64_150 sqrt-div_binary64_95
pow-exp_binary64_146 pow-to-exp_binary64_147 sqrt-pow1_binary64_96 flip-+_binary64_52 rem-sqrt-square_binary64_91 sqr-pow_binary64_50 pow1/2_binary64_158 flip3-+_binary64_81
Counts
4 → 58
Calls

8 calls:

5.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))
3.0ms
(pow.f64 (cbrt.f64 (sin.f64 ky)) 4)
1.0ms
(cbrt.f64 (sin.f64 ky))
1.0ms
(cbrt.f64 (sin.f64 ky))
0.0ms
(+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2)))

series495.0ms (3.2%)

Counts
4 → 29
Calls

4 calls:

190.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))
137.0ms
(pow.f64 (cbrt.f64 (sin.f64 ky)) 4)
84.0ms
(cbrt.f64 (sin.f64 ky))
83.0ms
(cbrt.f64 (sin.f64 ky))
Compiler

Compiled 1096 to 914 computations (16.6% saved)

simplify76.0ms (0.5%)

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049301252
149301252

prune108.0ms (0.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New87087
Fresh01010
Picked011
Done022
Total8713100
Error
1.1b
Counts
100 → 13
Compiler

Compiled 2294 to 1227 computations (46.5% saved)

simplify30.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
03902123
13902123

regimes973.0ms (6.3%)

Compiler

Compiled 11280 to 8998 computations (20.2% saved)

bsearch0.0ms (0%)

regimes481.0ms (3.1%)

Compiler

Compiled 1150 to 1162 computations (-1% saved)

bsearch2.0ms (0%)

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes314.0ms (2%)

Compiler

Compiled 691 to 749 computations (-8.4% saved)

bsearch1.0ms (0%)

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes174.0ms (1.1%)

Compiler

Compiled 410 to 460 computations (-12.2% saved)

bsearch1.0ms (0%)

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes192.0ms (1.2%)

Compiler

Compiled 320 to 388 computations (-21.3% saved)

bsearch1.0ms (0%)

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes127.0ms (0.8%)

Compiler

Compiled 74 to 149 computations (-101.4% saved)

bsearch130.0ms (0.8%)

Steps
ItersRangePoint
8
6.718092772816654e-184
5.389020933597463e-180
4.9006235456263095e-180
7
-0.00031753722337157916
-1.42608262710057e-05
-0.0003133110752946284
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes90.0ms (0.6%)

Compiler

Compiled 30 to 90 computations (-200% saved)

bsearch174.0ms (1.1%)

Steps
ItersRangePoint
8
6.718092772816654e-184
5.389020933597463e-180
6.870969801265937e-182
11
-4.890056274766595e+16
-0.00031753722337157916
-3183254.7726675374
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes23.0ms (0.1%)

Accuracy

Total 2.3b remaining (56.9%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch13.0ms (0.1%)

Compiler

Compiled 191 to 134 computations (29.8% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073300
173300

end0.0ms (0%)

sample6.2s (39.7%)

Algorithm
intervals
Results
3.4s4622×body1024valid
636.0ms1428×body512valid
188.0ms1409×body128valid
145.0ms521×body256valid
25.0ms20×body2048valid
Compiler

Compiled 1450 to 1142 computations (21.2% saved)

Pareto

-0.11259435851389907

Profiling

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