Details

Time bar (total: 12.2s)

analyze854.0ms (7%)

Algorithm
1×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)

sample4.0s (32.9%)

Results
2.1s6557×body128valid
1.1s800×body1024valid
548.0ms581×body512valid
209.0ms318×body256valid
Compiler

Compiled 68 to 60 computations (11.8% saved)

preprocess41.0ms (0.3%)

Algorithm
2×egg-herbie
Rules
714×fma-def_binary64
500×unswap-sqr_binary64
324×associate-*l/_binary64
288×associate-*r/_binary64
262×associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
088294
1237259
2654259
33190259
044
144
Stop Event
1×unsound
1×node limit
Symmetry

(sort kx ky)

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify22.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
665×fma-def_binary64
578×associate-*l*_binary64
512×unswap-sqr_binary64
433×associate-*r*_binary64
328×associate-*l/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02442
15637
212637
358037
4338637
Stop Event
1×node limit
Counts
1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
1.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶1.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 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)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(pow.f64 (sin.f64 kx) 2)
✓0.5b
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
✓1.9b
(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓8.4b
(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series689.0ms (5.7%)

Counts
4 → 148
Calls

39 calls:

74.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
kx
inf
73.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
kx
-inf
73.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
ky
-inf
68.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
ky
inf
41.0ms
(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
kx
-inf

rewrite75.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
653×prod-diff_binary64
189×add-sqr-sqrt_binary64
184×log1p-expm1-u_binary64
184×expm1-log1p-u_binary64
180×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01994
140285
2492085
Stop Event
1×node limit
Counts
4 → 93

simplify168.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
424×fma-neg_binary64
336×fma-def_binary64
266×*-commutative_binary64
261×associate-*r*_binary64
192×associate-*r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037311132
1121910267
2488710261
Stop Event
1×node limit
Counts
241 → 221

prune374.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2183221
Fresh000
Picked011
Done000
Total2184222
Error
0b
Counts
222 → 4
Alt Table
StatusErrorProgram
32.3b
(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 (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))))) (/.f64 1/2 l))))))
✓1.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
▶10.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1)))))
29.3b
(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 12392 to 8571 computations (30.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓3.6b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
✓5.9b
(sqrt.f64 (fma.f64 (*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1))
✓6.5b
(*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))
✓7.0b
(/.f64 (*.f64 l l) Om)

series152.0ms (1.2%)

Counts
4 → 100
Calls

30 calls:

15.0ms
(sqrt.f64 (fma.f64 (*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1))
ky
-inf
15.0ms
(sqrt.f64 (fma.f64 (*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1))
ky
inf
10.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))
ky
-inf
9.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))
l
0
9.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))
l
-inf

rewrite65.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
248×expm1-udef_binary64
248×log1p-udef_binary64
147×egg-rr
142×add-sqr-sqrt_binary64
137×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01558
130952
2388052
Stop Event
1×node limit
Counts
4 → 147

simplify50.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
744×associate-/l*_binary64
573×associate-/r*_binary64
255×fma-def_binary64
207×associate-*l/_binary64
178×associate-/r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01272317
13952267
214982234
Stop Event
1×node limit
Counts
247 → 197

prune275.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1952197
Fresh202
Picked101
Done011
Total1983201
Error
0b
Counts
201 → 3
Alt Table
StatusErrorProgram
▶5.3b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))))
✓1.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
16.1b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 (/.f64 (*.f64 l l) Om) (*.f64 (/.f64 ky Om) ky)) 4 1)))))
Compiler

Compiled 5352 to 3501 computations (34.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))
✓2.9b
(/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om)
✓4.9b
(/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om)
✓5.9b
(sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1))

series319.0ms (2.6%)

Counts
4 → 144
Calls

36 calls:

57.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))
ky
inf
42.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))
ky
-inf
15.0ms
(sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1))
ky
-inf
15.0ms
(sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1))
ky
inf
13.0ms
(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))
l
inf

rewrite78.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
269×expm1-udef_binary64
269×log1p-udef_binary64
152×add-sqr-sqrt_binary64
148×log1p-expm1-u_binary64
148×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01672
133363
2399663
Stop Event
1×node limit
Counts
4 → 122

simplify77.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
876×associate-/l*_binary64
447×fma-def_binary64
322×cancel-sign-sub-inv_binary64
254×associate-/r/_binary64
184×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01724069
15553983
221093938
Stop Event
1×node limit
Counts
266 → 204

prune243.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2031204
Fresh101
Picked101
Done011
Total2052207
Error
0b
Counts
207 → 2
Alt Table
StatusErrorProgram
✓1.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
▶3.6b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1)))))))
Compiler

Compiled 5719 to 3788 computations (33.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2)
✓0.7b
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))
✓2.7b
(/.f64 (*.f64 l (sin.f64 ky)) Om)
✓5.9b
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))

series148.0ms (1.2%)

Counts
4 → 112
Calls

36 calls:

11.0ms
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))
ky
inf
10.0ms
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))
ky
-inf
9.0ms
(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))
ky
inf
8.0ms
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))
ky
-inf
7.0ms
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))
Om
inf

rewrite68.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
610×log-prod_binary64
224×expm1-udef_binary64
224×log1p-udef_binary64
205×log-pow_binary64
160×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01557
128157
2322457
Stop Event
1×node limit
Counts
4 → 160

simplify64.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
809×associate-/l*_binary64
613×associate-/r*_binary64
271×fma-def_binary64
206×associate-/r/_binary64
162×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01373450
14303362
215963304
Stop Event
1×node limit
Counts
272 → 179

prune181.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1790179
Fresh000
Picked011
Done011
Total1792181
Error
0b
Counts
181 → 2
Alt Table
StatusErrorProgram
✓1.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
✓3.6b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1)))))))
Compiler

Compiled 5065 to 3333 computations (34.2% saved)

regimes4.0s (33.2%)

Accuracy

Total 0.7b remaining (83.3%)

Threshold costs 0.7b (83.3%)

Counts
151 → 3
Compiler

Compiled 78770 to 64717 computations (17.8% saved)

bsearch6.0ms (0.1%)

Algorithm
2×left-value
Calls

2 calls:

0.0ms
(sin.f64 kx)
0.0ms
(sin.f64 kx)
Steps
ItersPointRange
-5.174496557575073e-305
∈ [
-5.174496557575073e-305
, 
9.61966246705209e-291
]
-5.98664871367318e-76
∈ [
-5.98664871367318e-76
, 
-4.7307516232512617e-76
]
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
039114
145114
Stop Event
1×saturated

end114.0ms (0.9%)

Stop Event
1×done
Remove

(sort kx ky)

Compiler

Compiled 359 to 272 computations (24.2% saved)

Profiling

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