Details

Time bar (total: 15.1s)

analyze1.4s (9.1%)

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)

sample164.0ms (1.1%)

Algorithm
intervals
Results
114.0ms154×body1024valid
26.0ms44×body512valid
6.0ms45×body128valid
4.0ms13×body256valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify108.0ms (0.7%)

Algorithm
egg-herbie
Rules
645×associate-/r*_binary64
634×sqr-pow_binary64
437×cube-prod_binary64
394×associate-*l*_binary64
368×*-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
12626
23626
36426
413326
533626
6103526
7173226
8242026
9263326
10290426
11325926
12365326
13455526
14487326
15487526

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
5.2b
Counts
1 → 1
Alt Table
StatusErrorProgram
5.2b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
Compiler

Compiled 38 to 28 computations (26.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.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
(pow.f64 (sin.f64 kx) 2)
0.3b
(pow.f64 (sin.f64 ky) 2)
4.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite206.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
4.9b
Rules
41×*-un-lft-identity_binary64
34×add-sqr-sqrt_binary64
30×associate-*l*_binary64
26×times-frac_binary64
25×add-cube-cbrt_binary64
Counts
4 → 103
Calls

4 calls:

17.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms
(pow.f64 (sin.f64 ky) 2)
3.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 2434 to 1345 computations (44.7% saved)

series216.0ms (1.4%)

Error
2.5b
Counts
4 → 33
Calls

4 calls:

125.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
45.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms
(pow.f64 (sin.f64 ky) 2)
7.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 2095 to 1419 computations (32.3% saved)

simplify152.0ms (1%)

Algorithm
egg-herbie
Rules
701×associate-/l*_binary64
532×associate-/r*_binary64
289×cancel-sign-sub-inv_binary64
144×associate-/r/_binary64
122×distribute-rgt-neg-in_binary64
Counts
136 → 95
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02363257
15772992
217812884
347062884
449872884
549562884

prune127.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New801595
Fresh000
Picked101
Done000
Total811596
Error
2.4b
Counts
96 → 15
Alt Table
StatusErrorProgram
37.0b
(*.f64 (sqrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sqrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
27.0b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) 3))
38.1b
(log.f64 (exp.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
5.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
38.2b
(exp.f64 (log.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
6.0b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
12.4b
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (sin.f64 th))
5.7b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))) (sin.f64 th))
7.8b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))) (sin.f64 th))
47.7b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
35.5b
(*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
48.8b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
46.1b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
5.2b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
32.4b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (-.f64 th (*.f64 1/6 (pow.f64 th 3))))
Compiler

Compiled 2524 to 1500 computations (40.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (sin.f64 ky) 2)
0.3b
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite236.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
2.4b
Rules
72×*-un-lft-identity_binary64
50×times-frac_binary64
49×add-sqr-sqrt_binary64
41×sqrt-prod_binary64
40×add-cube-cbrt_binary64
Counts
4 → 134
Calls

4 calls:

22.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 3290 to 1810 computations (45% saved)

series325.0ms (2.2%)

Error
2.4b
Counts
4 → 45
Calls

4 calls:

125.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
106.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
43.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 2975 to 2021 computations (32.1% saved)

simplify206.0ms (1.4%)

Algorithm
egg-herbie
Rules
613×associate-/r*_binary64
390×cancel-sign-sub-inv_binary64
267×associate-/r/_binary64
190×associate-*r*_binary64
182×distribute-rgt-neg-in_binary64
Counts
179 → 99
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02715131
16814708
224104549
348284549
449974549
549494549

prune111.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New95499
Fresh6814
Picked101
Done000
Total10212114
Error
2.4b
Counts
114 → 12
Alt Table
StatusErrorProgram
5.4b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
37.0b
(*.f64 (sqrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sqrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
38.1b
(log.f64 (exp.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
5.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
38.2b
(exp.f64 (log.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
6.0b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
7.9b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))))
5.8b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
47.7b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
48.8b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
46.1b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
5.7b
(*.f64 (/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
Compiler

Compiled 2143 to 1264 computations (41% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
0.4b
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.7b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite392.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
2.4b
Rules
164×sqrt-prod_binary64
130×add-sqr-sqrt_binary64
123×times-frac_binary64
120×*-un-lft-identity_binary64
72×add-cube-cbrt_binary64
Counts
4 → 209
Calls

4 calls:

54.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
13.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Compiler

Compiled 7412 to 4466 computations (39.7% saved)

series377.0ms (2.5%)

Error
2.4b
Counts
4 → 44
Calls

4 calls:

125.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
113.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
51.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
49.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Compiler

Compiled 3802 to 2616 computations (31.2% saved)

simplify309.0ms (2%)

Algorithm
egg-herbie
Rules
774×times-frac_binary64
409×cancel-sign-sub-inv_binary64
193×associate-/l*_binary64
192×*-commutative_binary64
190×neg-mul-1_binary64 neg-sub0_binary64
Counts
253 → 133
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
031711248
185610032
2268910008
3449110002
4493310002

prune148.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1294133
Fresh3811
Picked101
Done000
Total13312145
Error
2.4b
Counts
145 → 12
Alt Table
StatusErrorProgram
38.8b
(exp.f64 (log.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
7.8b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3)))))
49.5b
(-.f64 (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)) (+.f64 (*.f64 1/2 (/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 kx) ky) 3))) (*.f64 1/6 (/.f64 (*.f64 (pow.f64 ky 3) (sin.f64 th)) (sin.f64 kx)))))
5.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
6.0b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
7.9b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))))
5.8b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
47.7b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
48.8b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
46.1b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
6.0b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
5.7b
(*.f64 (/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
Compiler

Compiled 3622 to 2200 computations (39.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (sin.f64 kx))
0.6b
(cbrt.f64 (sin.f64 kx))
0.8b
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.7b
(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite110.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
2.4b
Rules
11×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64
cbrt-prod_binary64
pow1_binary64 unpow-prod-down_binary64
add-exp-log_binary64
Counts
4 → 58
Calls

4 calls:

10.0ms
(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
1.0ms
(cbrt.f64 (sin.f64 kx))
1.0ms
(cbrt.f64 (sin.f64 kx))
Compiler

Compiled 1737 to 865 computations (50.2% saved)

series108.0ms (0.7%)

Error
2.4b
Counts
4 → 19
Calls

4 calls:

44.0ms
(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
19.0ms
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
17.0ms
(cbrt.f64 (sin.f64 kx))
14.0ms
(cbrt.f64 (sin.f64 kx))
Compiler

Compiled 1224 to 846 computations (30.9% saved)

simplify97.0ms (0.6%)

Algorithm
egg-herbie
Rules
479×times-frac_binary64
457×associate-*l*_binary64
353×associate-*r*_binary64
318×distribute-neg-frac_binary64
279×associate-/r*_binary64
Counts
77 → 51
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01131254
1252961
2669917
33293914
44582914
54904914

prune69.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New51051
Fresh01111
Picked011
Done000
Total511263
Error
2.4b
Counts
63 → 12
Alt Table
StatusErrorProgram
38.8b
(exp.f64 (log.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
7.8b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3)))))
49.5b
(-.f64 (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)) (+.f64 (*.f64 1/2 (/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 kx) ky) 3))) (*.f64 1/6 (/.f64 (*.f64 (pow.f64 ky 3) (sin.f64 th)) (sin.f64 kx)))))
5.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
6.0b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
7.9b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))))
5.8b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
47.7b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
48.8b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
46.1b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
6.0b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
5.7b
(*.f64 (/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
Compiler

Compiled 1269 to 731 computations (42.4% saved)

regimes4.9s (32.6%)

Accuracy

Total 2.3b remaining (55.8%)

Threshold costs 0b (0%)

Compiler

Compiled 64956 to 46307 computations (28.7% saved)

bsearch13.0ms (0.1%)

Compiler

Compiled 16 to 12 computations (25% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01955
12155
22155

end1.0ms (0%)

Compiler

Compiled 37 to 24 computations (35.1% saved)

sample5.3s (34.8%)

Algorithm
intervals
Results
3.5s4653×body1024valid
676.0ms1399×body512valid
179.0ms1405×body128valid
157.0ms520×body256valid
35.0ms23×body2048valid
Compiler

Compiled 380 to 268 computations (29.5% saved)

Profiling

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