Details

Time bar (total: 14.5s)

analyze1.8s (12.6%)

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 20 to 15 computations (25% saved)

sample8.2s (56.8%)

Results
6.3s4772×body1024valid
1.1s1472×body512valid
367.0ms1485×body128valid
248.0ms513×body256valid
30.0ms14×body2048valid
Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify72.0ms (0.5%)

Algorithm
egg-herbie
Rules
645×associate-/r*_binary64
634×sqr-pow_binary64
394×associate-*l*_binary64
373×cube-prod_binary64
368×*-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01426
12618
24018
36818
414118
534818
6105518
7179618
8248418
9269718
10296818
11331118
12370518
13460318
14479918
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
3.2b
(*.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
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Compiler

Compiled 96 to 63 computations (34.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
0.2b
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series275.0ms (1.9%)

Counts
3 → 84
Calls

3 calls:

153.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
97.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
25.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite70.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
525×log-prod_binary64
330×prod-diff_binary64
191×expm1-udef_binary64
191×log1p-udef_binary64
180×pow3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
120339
2251439
3492339
4534839
Stop Event
node limit
Counts
3 → 88
Calls

3 calls:

68.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
68.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
68.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify86.0ms (0.6%)

Algorithm
egg-herbie
Rules
852×fma-def_binary64
469×cancel-sign-sub-inv_binary64
357×fma-neg_binary64
281×neg-mul-1_binary64
205×sub-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02332944
17202800
226632590
345792590
449782590
Stop Event
node limit
Counts
172 → 145

prune201.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1369145
Fresh101
Picked101
Done000
Total1389147
Error
0.0b
Counts
147 → 9
Alt Table
StatusErrorProgram
0.3b
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
1.3b
(*.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) 1) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.5b
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2)) (sin.f64 th))
27.7b
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) 2)
3.3b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
2.6b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
Compiler

Compiled 3996 to 1877 computations (53% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.2b
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
0.2b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series193.0ms (1.3%)

Counts
2 → 60
Calls

2 calls:

153.0ms
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
40.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite52.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
570×log-prod_binary64
197×expm1-udef_binary64
197×log1p-udef_binary64
183×log-pow_binary64
171×prod-diff_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01031
120931
2272831
3517631
Stop Event
node limit
Counts
2 → 82
Calls

2 calls:

51.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
51.0ms
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

simplify77.0ms (0.5%)

Algorithm
egg-herbie
Rules
852×times-frac_binary64
776×fma-def_binary64
346×cancel-sign-sub-inv_binary64
322×fma-neg_binary64
138×sub-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01912346
15852158
221542148
349822146
451412146
Stop Event
node limit
Counts
142 → 123

prune176.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1592161
Fresh268
Picked011
Done000
Total1619170
Error
0b
Counts
170 → 9
Alt Table
StatusErrorProgram
0.3b
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.5b
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2)) (sin.f64 th))
34.4b
(fma.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (*.f64 (sin.f64 ky) (pow.f64 th 5)) 1/120) (fma.f64 (*.f64 (sin.f64 ky) (pow.f64 th 7)) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) -1/5040) (*.f64 (*.f64 (sin.f64 ky) (pow.f64 th 3)) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) -1/6)))))
27.7b
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) 2)
0.7b
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
2.6b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
Compiler

Compiled 4532 to 2017 computations (55.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
0.1b
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.1b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
0.2b
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series325.0ms (2.2%)

Counts
2 → 72
Calls

2 calls:

172.0ms
(expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
153.0ms
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

rewrite53.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
563×log-prod_binary64
206×expm1-udef_binary64
206×log1p-udef_binary64
204×prod-diff_binary64
193×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01238
122238
2270538
3509638
Stop Event
node limit
Counts
2 → 74
Calls

2 calls:

51.0ms
(expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
51.0ms
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

simplify99.0ms (0.7%)

Algorithm
egg-herbie
Rules
435×cancel-sign-sub-inv_binary64
412×fma-neg_binary64
254×neg-mul-1_binary64
229×associate-*r*_binary64
199×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02603511
18243491
231743276
346173276
450253276
Stop Event
node limit
Counts
146 → 118

prune226.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2232225
Fresh257
Picked011
Done011
Total2259234
Error
0b
Counts
234 → 9
Alt Table
StatusErrorProgram
0.8b
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.7b
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
0.3b
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.5b
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
3.3b
(log1p.f64 (expm1.f64 (*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))))
27.7b
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) 2)
2.6b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
Compiler

Compiled 7346 to 3420 computations (53.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
0.2b
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.3b
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))

series334.0ms (2.3%)

Counts
3 → 84
Calls

3 calls:

155.0ms
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
94.0ms
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
85.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite52.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
574×log-prod_binary64
209×expm1-udef_binary64
209×log1p-udef_binary64
197×log-pow_binary64
160×prod-diff_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01242
123742
2271542
3498542
Stop Event
node limit
Counts
3 → 76
Calls

3 calls:

51.0ms
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
51.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
51.0ms
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))

simplify94.0ms (0.6%)

Algorithm
egg-herbie
Rules
517×fma-neg_binary64
427×cancel-sign-sub-inv_binary64
277×associate-/r/_binary64
206×sub-neg_binary64
194×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02313062
17173038
227042849
349082849
452092849
Stop Event
node limit
Counts
160 → 132

prune170.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1691170
Fresh156
Picked011
Done022
Total1709179
Error
0b
Counts
179 → 9
Alt Table
StatusErrorProgram
0.8b
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.7b
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
0.3b
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.5b
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
27.7b
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) 2)
3.3b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
2.6b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
Compiler

Compiled 4658 to 2334 computations (49.9% saved)

regimes1.7s (11.7%)

Accuracy

Total 0.2b remaining (85.3%)

Threshold costs 0.2b (85.3%)

Counts
162 → 1
Compiler

Compiled 28964 to 19277 computations (33.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11118
21118
Stop Event
saturated

end137.0ms (0.9%)

Compiler

Compiled 206 to 127 computations (38.3% saved)

Profiling

Loading profile data...