Details

Time bar (total: 16.4s)

analyze724.0ms (4.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
49.9%49.9%0.2%3
49.9%49.9%0.2%4
49.9%49.9%0.2%5
49.9%49.9%0.2%6
74.9%25%0.2%7
74.9%25%0.2%8
74.9%25%0.2%9
74.9%25%0.2%10
87.3%12.5%0.2%11
87.3%12.5%0.2%12
87.3%12.5%0.2%13
87.3%12.5%0.2%14
Compiler

Compiled 34 to 30 computations (11.8% saved)

sample91.0ms (0.6%)

Algorithm
intervals
Results
33.0ms197×body128valid
20.0ms25×body1024valid
12.0ms21×body512valid
5.0ms13×body256valid
Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify63.0ms (0.4%)

Algorithm
egg-herbie
Rules
575×associate-*l*_binary64
512×unswap-sqr_binary64
437×associate-*r*_binary64
407×distribute-rgt-out_binary64
369×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02442
15639
210739
342939
4203739
5485039
6480939
7552339

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
2.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
2.3b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
Compiler

Compiled 87 to 75 computations (13.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (sin.f64 kx) 2)
0.3b
(/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.4b
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.1b
(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite284.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
1.9b
Rules
33×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
21×times-frac_binary64
19×add-exp-log_binary64
Counts
4 → 113
Calls

4 calls:

17.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms
(/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.0ms
(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 4229 to 3201 computations (24.3% saved)

series745.0ms (4.5%)

Error
0.6b
Counts
4 → 56
Calls

4 calls:

343.0ms
(/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
217.0ms
(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
115.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 5726 to 4733 computations (17.3% saved)

simplify158.0ms (1%)

Algorithm
egg-herbie
Rules
432×distribute-rgt-in_binary64
420×distribute-lft-in_binary64
359×times-frac_binary64
304×unswap-sqr_binary64
178×associate-*r*_binary64
Counts
169 → 144
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03046442
17196047
221875859
352315859

prune199.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1413144
Fresh000
Picked011
Done000
Total1414145
Error
0b
Counts
145 → 4
Alt Table
StatusErrorProgram
27.7b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (*.f64 l (sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
5.6b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
Compiler

Compiled 3895 to 2854 computations (26.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))
2.3b
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))
3.4b
(*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))
9.1b
(sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))))

rewrite346.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
45×add-sqr-sqrt_binary64
42×*-un-lft-identity_binary64
39×times-frac_binary64
38×add-cube-cbrt_binary64
25×log-pow_binary64
Counts
4 → 129
Calls

4 calls:

19.0ms
(*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))
9.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))
6.0ms
(/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))
4.0ms
(sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))))
Compiler

Compiled 5472 to 4213 computations (23% saved)

series1.3s (7.7%)

Error
0b
Counts
4 → 69
Calls

4 calls:

543.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))
307.0ms
(/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))
218.0ms
(sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))))
119.0ms
(*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))
Compiler

Compiled 7391 to 6151 computations (16.8% saved)

simplify304.0ms (1.9%)

Algorithm
egg-herbie
Rules
390×distribute-rgt-in_binary64
390×times-frac_binary64
382×distribute-lft-in_binary64
153×unswap-sqr_binary64
148×associate-*r*_binary64
Counts
198 → 180
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03448267
16817771
219197496
347807490
449977490
549627490

prune278.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1800180
Fresh022
Picked011
Done011
Total1804184
Error
0b
Counts
184 → 4
Alt Table
StatusErrorProgram
27.7b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (*.f64 l (sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
5.6b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
Compiler

Compiled 5360 to 3973 computations (25.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
4.6b
(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.1b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
7.9b
(/.f64 (*.f64 l l) Om)

rewrite411.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
67×times-frac_binary64
61×*-un-lft-identity_binary64
51×add-sqr-sqrt_binary64
47×add-cube-cbrt_binary64
30×unpow-prod-down_binary64
Counts
4 → 163
Calls

4 calls:

57.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
6.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
6.0ms
(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.0ms
(/.f64 (*.f64 l l) Om)
Compiler

Compiled 5891 to 3454 computations (41.4% saved)

series227.0ms (1.4%)

Error
0b
Counts
4 → 32
Calls

4 calls:

128.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
29.0ms
(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
25.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
23.0ms
(/.f64 (*.f64 l l) Om)
Compiler

Compiled 2340 to 1870 computations (20.1% saved)

simplify157.0ms (1%)

Algorithm
egg-herbie
Rules
505×associate-/l/_binary64
369×associate-/r/_binary64
338×distribute-rgt-in_binary64
320×distribute-lft-in_binary64
206×associate-*l/_binary64
Counts
195 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02814132
16543504
221543414
348483414
449983414

prune146.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1270127
Fresh011
Picked011
Done022
Total1274131
Error
0b
Counts
131 → 4
Alt Table
StatusErrorProgram
27.7b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (*.f64 l (sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
5.6b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
Compiler

Compiled 2712 to 1607 computations (40.7% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.1b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.1b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
27.1b
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
27.2b
(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite413.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
51×times-frac_binary64
41×add-sqr-sqrt_binary64
40×*-un-lft-identity_binary64
40×add-cube-cbrt_binary64
24×unpow-prod-down_binary64
Counts
4 → 144
Calls

4 calls:

53.0ms
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
46.0ms
(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
6.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
6.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
Compiler

Compiled 8249 to 5463 computations (33.8% saved)

series338.0ms (2.1%)

Error
0b
Counts
4 → 35
Calls

4 calls:

128.0ms
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
112.0ms
(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
31.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
29.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
Compiler

Compiled 4409 to 3208 computations (27.2% saved)

simplify122.0ms (0.7%)

Algorithm
egg-herbie
Rules
554×times-frac_binary64
537×associate-/l*_binary64
368×associate-*l/_binary64
354×associate-*l*_binary64
347×associate-/r*_binary64
Counts
179 → 110
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02374112
14923679
212923638
350033638

prune170.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1100110
Fresh000
Picked011
Done033
Total1104114
Error
0b
Counts
114 → 4
Alt Table
StatusErrorProgram
27.7b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (*.f64 l (sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
5.6b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2)))))))))
2.3b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
Compiler

Compiled 4805 to 3154 computations (34.4% saved)

regimes6.8s (41.6%)

Accuracy

Total 0.3b remaining (78.3%)

Threshold costs 0.3b (78.3%)

Compiler

Compiled 128438 to 101259 computations (21.2% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049201
165201
264201

end15.0ms (0.1%)

Remove

(sort kx ky)

Compiler

Compiled 396 to 300 computations (24.2% saved)

sample3.0s (18.3%)

Algorithm
intervals
Results
1.3s6390×body128valid
657.0ms786×body1024valid
311.0ms526×body512valid
121.0ms296×body256valid
2.0msbody2048valid
Compiler

Compiled 316 to 251 computations (20.6% saved)

Profiling

Loading profile data...