Details

Time bar (total: 23.7s)

analyze1.8s (7.4%)

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)

sample225.0ms (0.9%)

Algorithm
intervals
Results
86.0ms196×body128valid
70.0ms31×body1024valid
27.0ms19×body512valid
9.0ms10×body256valid
Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify67.0ms (0.3%)

Algorithm
egg-herbie
Rules
665×fma-def_binary64
575×associate-*l*_binary64
512×unswap-sqr_binary64
437×associate-*r*_binary64
369×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02442
15637
211337
346537
4214937
5498237
6484737
7496437

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
1.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
1.5b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
Compiler

Compiled 113 to 95 computations (15.9% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
0.3b
(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
2.2b
(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
10.7b
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series2.4s (9.9%)

Counts
4 → 168
Calls

4 calls:

1.7s
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
443.0ms
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
201.0ms
(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
26.0ms
(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

rewrite29.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
23×*-un-lft-identity_binary64
23×add-cube-cbrt_binary64
21×times-frac_binary64
15×sqrt-prod_binary64
Counts
4 → 92
Calls

4 calls:

8.0ms
(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
6.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
2.0ms
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
1.0ms
(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

simplify478.0ms (2%)

Algorithm
egg-herbie
Rules
396×fma-neg_binary64
329×fma-def_binary64
271×associate-*r*_binary64
206×associate-*r/_binary64
199×associate-*l*_binary64
Counts
260 → 226
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049314676
1139713058
2498413052
3528313052

prune780.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2215226
Fresh000
Picked101
Done000
Total2225227
Error
0b
Counts
227 → 5
Alt Table
StatusErrorProgram
1.5b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))
1.5b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))))))
27.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (*.f64 Om (sqrt.f64 (/.f64 1/4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
32.4b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (*.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))))) l))))))
16.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 (*.f64 4 (/.f64 (*.f64 (pow.f64 l 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 Om 2))) 1)))))
Compiler

Compiled 13089 to 9705 computations (25.9% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
2.2b
(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
7.6b
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))
10.7b
(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3)))

series639.0ms (2.7%)

Counts
2 → 96
Calls

2 calls:

435.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3)))
202.0ms
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod_binary64
15×sqrt-prod_binary64
13×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 55
Calls

2 calls:

5.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3)))
3.0ms
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))

simplify490.0ms (2.1%)

Algorithm
egg-herbie
Rules
451×cancel-sign-sub-inv_binary64
296×unswap-sqr_binary64
263×fma-neg_binary64
200×associate-*r*_binary64
187×fma-def_binary64
Counts
151 → 140
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03128631
18627936
232897913
348547913
449807913
549987913
649587913

prune676.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2051206
Fresh134
Picked011
Done000
Total2065211
Error
0b
Counts
211 → 5
Alt Table
StatusErrorProgram
32.4b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (*.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))))) l))))))
16.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1)))))
1.5b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))
1.5b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))))))
27.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (*.f64 Om (sqrt.f64 (/.f64 1/4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
Compiler

Compiled 10483 to 7655 computations (27% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
2.2b
(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
2.6b
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
10.7b
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series1.7s (7%)

Counts
1 → 48
Calls

1 calls:

1.7s
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

rewrite20.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×log-pow_binary64
22×exp-prod_binary64
18×times-frac_binary64
15×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
Counts
1 → 36
Calls

1 calls:

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

simplify237.0ms (1%)

Algorithm
egg-herbie
Rules
838×fma-def_binary64
318×cancel-sign-sub-inv_binary64
252×unswap-sqr_binary64
197×fma-neg_binary64
161×associate-*r*_binary64
Counts
84 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03285968
18395642
229405606
349815606

prune826.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2380238
Fresh033
Picked011
Done011
Total2385243
Error
0b
Counts
243 → 5
Alt Table
StatusErrorProgram
32.4b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (*.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))))) l))))))
16.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1)))))
1.5b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))
1.5b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))))))
27.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (*.f64 Om (sqrt.f64 (/.f64 1/4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
Compiler

Compiled 14126 to 10433 computations (26.1% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1)))
8.0b
(sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1))
10.2b
(*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2))
14.7b
(/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om))

series828.0ms (3.5%)

Counts
4 → 132
Calls

4 calls:

458.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1)))
168.0ms
(sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1))
163.0ms
(/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om))
37.0ms
(*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2))

rewrite54.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
68×add-exp-log_binary64
34×prod-exp_binary64
32×add-cbrt-cube_binary64
25×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
Counts
4 → 123
Calls

4 calls:

14.0ms
(/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om))
12.0ms
(*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2))
5.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1)))
2.0ms
(sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1))

simplify338.0ms (1.4%)

Algorithm
egg-herbie
Rules
735×fma-def_binary64
357×times-frac_binary64
273×fma-neg_binary64
252×unswap-sqr_binary64
217×associate-/l*_binary64
Counts
255 → 214
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03287385
18296850
233546758
348406714
449606714

prune483.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2131214
Fresh202
Picked011
Done022
Total2154219
Error
0b
Counts
219 → 4
Alt Table
StatusErrorProgram
1.5b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))
1.5b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1) 3))))))
27.7b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (/.f64 (*.f64 l (sin.f64 kx)) Om) (*.f64 1/4 (/.f64 Om (*.f64 l (sin.f64 kx))))))))
16.9b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 l l) (pow.f64 (sin.f64 kx) 2)) (*.f64 Om Om)) 4 1)))))
Compiler

Compiled 7087 to 4449 computations (37.2% saved)

regimes4.7s (19.9%)

Accuracy

Total 0.1b remaining (18.7%)

Threshold costs 0.1b (18.7%)

Counts
104 → 2
Compiler

Compiled 56057 to 46725 computations (16.6% saved)

bsearch10.0ms (0%)

Compiler

Compiled 21 to 17 computations (19% saved)

simplify7.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
038105
147105
246105

end23.0ms (0.1%)

Remove

(sort kx ky)

Compiler

Compiled 216 to 159 computations (26.4% saved)

sample6.8s (28.9%)

Algorithm
intervals
Results
2.9s6337×body128valid
1.8s778×body1024valid
888.0ms575×body512valid
308.0ms310×body256valid
Compiler

Compiled 221 to 177 computations (19.9% saved)

Profiling

Loading profile data...