Details

Time bar (total: 15.7s)

analyze1.8s (11.8%)

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)

sample210.0ms (1.3%)

Algorithm
intervals
Results
158.0ms151×body1024valid
28.0ms46×body512valid
9.0ms48×body128valid
4.0ms11×body256valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify103.0ms (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

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
3.5b
Counts
1 → 1
Alt Table
StatusErrorProgram
3.5b
(*.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)

localize15.0ms (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 ky) 2)
0.2b
(pow.f64 (sin.f64 kx) 2)
3.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite155.0ms (1%)

Algorithm
rewrite-expression-head
Error
3.3b
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:

15.0ms
(*.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)))
2.0ms
(pow.f64 (sin.f64 kx) 2)
2.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 2434 to 1345 computations (44.7% saved)

series173.0ms (1.1%)

Error
1.9b
Counts
4 → 37
Calls

4 calls:

101.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
31.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms
(pow.f64 (sin.f64 ky) 2)
8.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 2218 to 1513 computations (31.8% saved)

simplify149.0ms (0.9%)

Algorithm
egg-herbie
Rules
812×associate-/l*_binary64
345×cancel-sign-sub-inv_binary64
167×associate-/r/_binary64
148×associate-*r*_binary64
143×distribute-rgt-neg-in_binary64
Counts
140 → 99
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02733460
16653273
220513106
347163106
449833106
549483106

prune101.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New861399
Fresh000
Picked101
Done000
Total8713100
Error
1.7b
Counts
100 → 13
Alt Table
StatusErrorProgram
7.7b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))) (sin.f64 th))
3.9b
(*.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))
35.4b
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (*.f64 (sin.f64 th) (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
13.3b
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 (sin.f64 kx) 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))
4.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
5.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (sin.f64 th)))
38.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
44.9b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
4.7b
(*.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)))))))
31.5b
(*.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 (pow.f64 th 3) 1/6)))
48.6b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
47.3b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
3.6b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
Compiler

Compiled 2652 to 1564 computations (41% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (sin.f64 kx) 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)))))
3.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite189.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
1.7b
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:

17.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
7.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 3290 to 1815 computations (44.8% saved)

series275.0ms (1.7%)

Error
1.7b
Counts
4 → 48
Calls

4 calls:

105.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
92.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
32.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 3076 to 2083 computations (32.3% saved)

simplify824.0ms (5.2%)

Algorithm
egg-herbie
Rules
463×cancel-sign-sub-inv_binary64
339×associate-/r/_binary64
239×neg-mul-1_binary64
204×distribute-rgt-neg-in_binary64
197×associate-/l/_binary64
Counts
182 → 109
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03145439
17785175
226994913
347154913
450004913
549504913

prune86.0ms (0.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1045109
Fresh5712
Picked011
Done000
Total10913122
Error
1.7b
Counts
122 → 13
Alt Table
StatusErrorProgram
7.7b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))) (sin.f64 th))
3.9b
(*.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))
47.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))))
48.6b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
35.2b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 th))) (/.f64 (sqrt.f64 (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
38.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
44.9b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
4.1b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
13.3b
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 (sin.f64 kx) 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))
3.9b
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
5.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (sin.f64 th)))
3.6b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
35.4b
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sin.f64 ky))))
Compiler

Compiled 2424 to 1429 computations (41% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(cbrt.f64 (sin.f64 kx))
0.7b
(cbrt.f64 (sin.f64 kx))
0.7b
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
3.2b
(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)))

rewrite87.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
1.7b
Rules
11×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
cbrt-prod_binary64
unpow-prod-down_binary64
Counts
4 → 58
Calls

4 calls:

8.0ms
(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)))
2.0ms
(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
1.7b
Counts
4 → 24
Calls

4 calls:

30.0ms
(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)))
25.0ms
(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
18.0ms
(cbrt.f64 (sin.f64 kx))
17.0ms
(cbrt.f64 (sin.f64 kx))
Compiler

Compiled 1539 to 1082 computations (29.7% saved)

simplify74.0ms (0.5%)

Algorithm
egg-herbie
Rules
454×associate-*l*_binary64
448×distribute-rgt-neg-in_binary64
379×associate-*r*_binary64
229×times-frac_binary64
192×unswap-sqr_binary64
Counts
82 → 56
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01491414
13541121
28931071
335061068
448971068

prune63.0ms (0.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New56056
Fresh01111
Picked011
Done011
Total561369
Error
1.7b
Counts
69 → 13
Alt Table
StatusErrorProgram
7.7b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))) (sin.f64 th))
3.9b
(*.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))
47.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))))
48.6b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
35.2b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 th))) (/.f64 (sqrt.f64 (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
38.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
44.9b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
4.1b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
13.3b
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 (sin.f64 kx) 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))
3.9b
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
5.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (sin.f64 th)))
3.6b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
35.4b
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sin.f64 ky))))
Compiler

Compiled 1731 to 1038 computations (40% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 1 (+.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 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
0.3b
(*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.4b
(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite209.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
1.7b
Rules
77×*-un-lft-identity_binary64
49×times-frac_binary64
48×add-sqr-sqrt_binary64
45×sqrt-prod_binary64
35×add-cube-cbrt_binary64
Counts
4 → 139
Calls

4 calls:

15.0ms
(*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
13.0ms
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
10.0ms
(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms
(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
Compiler

Compiled 3601 to 2250 computations (37.5% saved)

series321.0ms (2%)

Error
1.7b
Counts
4 → 52
Calls

4 calls:

100.0ms
(*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
100.0ms
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
47.0ms
(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
39.0ms
(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Compiler

Compiled 3489 to 2388 computations (31.6% saved)

simplify165.0ms (1.1%)

Algorithm
egg-herbie
Rules
429×cancel-sign-sub-inv_binary64
298×associate-/r/_binary64
271×neg-mul-1_binary64
225×associate-*r*_binary64
198×distribute-rgt-neg-in_binary64
Counts
191 → 132
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02975631
17485382
226475141
348465141
449985141

prune109.0ms (0.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1311132
Fresh1910
Picked011
Done022
Total13213145
Error
1.7b
Counts
145 → 13
Alt Table
StatusErrorProgram
7.7b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (cbrt.f64 (pow.f64 (sin.f64 ky) 6))))) (sin.f64 th))
3.9b
(*.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))
4.3b
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sqrt.f64 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
3.9b
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
47.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))))
48.6b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
38.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2))))) (*.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
44.9b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
4.1b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
13.3b
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 (sin.f64 kx) 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))
5.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (sin.f64 th)))
3.6b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
35.4b
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sin.f64 ky))))
Compiler

Compiled 2705 to 1643 computations (39.3% saved)

regimes3.2s (20.5%)

Accuracy

Total 1.3b remaining (41.4%)

Threshold costs 0b (0%)

Compiler

Compiled 62784 to 44548 computations (29% saved)

bsearch12.0ms (0.1%)

Compiler

Compiled 16 to 12 computations (25% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02879
13579
23479

end1.0ms (0%)

Compiler

Compiled 52 to 31 computations (40.4% saved)

sample7.2s (45.6%)

Algorithm
intervals
Results
5.1s4649×body1024valid
896.0ms1400×body512valid
267.0ms553×body256valid
249.0ms1381×body128valid
37.0ms17×body2048valid
Compiler

Compiled 404 to 280 computations (30.7% saved)

Profiling

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