Details

Time bar (total: 12.0s)

analyze879.0ms (7.3%)

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
85.6%14%0.4%11
85.8%13.8%0.4%12
86%13.6%0.4%13
86.5%13.1%0.4%14
Compiler

Compiled 34 to 30 computations (11.8% saved)

sample3.9s (32.2%)

Results
2.0s6578×body128valid
1.1s776×body1024valid
534.0ms582×body512valid
198.0ms320×body256valid
Compiler

Compiled 68 to 60 computations (11.8% saved)

preprocess39.0ms (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)

simplify23.0ms (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

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.8b
(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)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.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)))
✓0.3b
(pow.f64 (sin.f64 kx) 2)
✓1.7b
(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓7.7b
(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))

series679.0ms (5.7%)

Counts
4 → 148
Calls

39 calls:

75.0ms
(/.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
75.0ms
(/.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
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
69.0ms
(/.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
34.0ms
(/.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
0

rewrite77.0ms (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

simplify179.0ms (1.5%)

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
2488610261
Stop Event
1×node limit
Counts
241 → 221

prune373.0ms (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
▶0.8b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))))
✓0.8b
(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)))))
30.2b
(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)))))
34.5b
(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))))))
Compiler

Compiled 12398 to 8578 computations (30.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
✓1.7b
(fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
✓2.5b
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))
✓7.7b
(sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))

series915.0ms (7.6%)

Counts
4 → 168
Calls

42 calls:

86.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))
kx
inf
85.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))
ky
-inf
84.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))
kx
-inf
82.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))
ky
inf
31.0ms
(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))
kx
0

rewrite76.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
327×log1p-udef_binary64
187×add-sqr-sqrt_binary64
180×log1p-expm1-u_binary64
180×expm1-log1p-u_binary64
176×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02190
140690
2456090
Stop Event
1×node limit
Counts
4 → 105

simplify193.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
417×fma-neg_binary64
356×fma-def_binary64
267×*-commutative_binary64
262×associate-*r*_binary64
197×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037711424
1123710553
2494610547
Stop Event
1×node limit
Counts
273 → 239

prune429.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2390239
Fresh022
Picked011
Done011
Total2394243
Error
0b
Counts
243 → 4
Alt Table
StatusErrorProgram
✓0.8b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))))
✓0.8b
(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)))))
▶30.2b
(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)))))
34.5b
(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))))))
Compiler

Compiled 13225 to 9082 computations (31.3% saved)

localize54.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓1.0b
(/.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)))
✓2.7b
(*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓27.7b
(sqrt.f64 (/.f64 1/4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓27.8b
(sqrt.f64 (*.f64 4 (*.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series881.0ms (7.3%)

Counts
4 → 156
Calls

39 calls:

100.0ms
(/.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)))
kx
-inf
88.0ms
(/.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)))
ky
-inf
86.0ms
(/.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)))
kx
inf
86.0ms
(/.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)))
ky
inf
56.0ms
(/.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)))
ky
0

rewrite50.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
243×add-sqr-sqrt_binary64
237×log1p-expm1-u_binary64
237×expm1-log1p-u_binary64
234×add-cbrt-cube_binary64
233×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
024132
1520113
Stop Event
1×node limit
Counts
4 → 79

simplify128.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
863×times-frac_binary64
520×associate-/l*_binary64
483×fma-def_binary64
203×*-commutative_binary64
101×+-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05289848
119029282
Stop Event
1×node limit
Counts
235 → 178

prune361.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2131214
Fresh101
Picked101
Done022
Total2153218
Error
0b
Counts
218 → 3
Alt Table
StatusErrorProgram
✓0.8b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))))
✓0.8b
(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)))))
▶30.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))))
Compiler

Compiled 15396 to 9008 computations (41.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))
✓0.7b
(/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))
✓1.2b
(*.f64 (/.f64 l Om) (sin.f64 ky))
✓1.2b
(/.f64 (/.f64 Om l) (sin.f64 ky))

series164.0ms (1.4%)

Counts
4 → 144
Calls

36 calls:

22.0ms
(/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))
ky
-inf
22.0ms
(/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))
ky
inf
8.0ms
(/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))
ky
0
5.0ms
(*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))
Om
0
5.0ms
(/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))
l
inf

rewrite73.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
284×log1p-udef_binary64
231×prod-diff_binary64
159×add-sqr-sqrt_binary64
150×add-log-exp_binary64
150×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01557
132557
2428257
Stop Event
1×node limit
Counts
4 → 120

simplify67.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
904×associate-/l*_binary64
424×fma-def_binary64
323×associate-/r/_binary64
171×cancel-sign-sub-inv_binary64
134×associate-/l/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01502888
14792864
219292846
Stop Event
1×node limit
Counts
264 → 173

prune155.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1730173
Fresh000
Picked011
Done022
Total1733176
Error
0b
Counts
176 → 3
Alt Table
StatusErrorProgram
✓0.8b
(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))))
✓0.8b
(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)))))
✓30.2b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (*.f64 (/.f64 l Om) (sin.f64 ky)) (*.f64 1/4 (/.f64 (/.f64 Om l) (sin.f64 ky)))))))
Compiler

Compiled 5004 to 2707 computations (45.9% saved)

regimes2.2s (18.1%)

Accuracy

Total 0.7b remaining (77.4%)

Threshold costs 0.7b (77.4%)

Counts
84 → 1
Compiler

Compiled 54706 to 42783 computations (21.8% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
2×*-commutative_binary64
1×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02336
13036
23236
33336
Stop Event
1×saturated

end108.0ms (0.9%)

Stop Event
1×done
Remove

(sort kx ky)

Compiler

Compiled 189 to 158 computations (16.4% saved)

Profiling

Loading profile data...