Details

Time bar (total: 14.6s)

analyze1.3s (9.2%)

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)

sample149.0ms (1%)

Algorithm
intervals
Results
108.0ms152×body1024valid
18.0ms40×body512valid
6.0ms49×body128valid
4.0ms15×body256valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify106.0ms (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
3.3b
Counts
1 → 1
Alt Table
StatusErrorProgram
3.3b
(*.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)

localize19.0ms (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)
0.3b
(pow.f64 (sin.f64 kx) 2)
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite197.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
3.1b
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)))
3.0ms
(pow.f64 (sin.f64 kx) 2)
3.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 2434 to 1345 computations (44.7% saved)

series197.0ms (1.3%)

Error
1.4b
Counts
4 → 33
Calls

4 calls:

109.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
43.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms
(pow.f64 (sin.f64 kx) 2)
9.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 1943 to 1331 computations (31.5% saved)

simplify123.0ms (0.8%)

Algorithm
egg-herbie
Rules
580×associate-/l*_binary64
427×associate-/r*_binary64
309×associate-*l/_binary64
256×associate-*r/_binary64
251×cancel-sign-sub-inv_binary64
Counts
136 → 95
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02233155
15372890
215852793
348702793
449572793

prune127.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New801595
Fresh000
Picked101
Done000
Total811596
Error
1.3b
Counts
96 → 15
Alt Table
StatusErrorProgram
3.6b
(*.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))
7.4b
(*.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))
3.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
3.9b
(*.f64 (/.f64 (sin.f64 ky) (*.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)))))) (sin.f64 th))
34.0b
(*.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))))))
3.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
5.0b
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
47.4b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
3.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
31.8b
(*.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)))))))
48.2b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
44.2b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
4.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (cbrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (cbrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
37.3b
(*.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)))))
33.7b
(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)))))))
Compiler

Compiled 2627 to 1552 computations (40.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(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)))))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite253.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
1.2b
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)))))
12.0ms
(/.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 kx) 2)
Compiler

Compiled 3290 to 1815 computations (44.8% saved)

series303.0ms (2.1%)

Error
1.2b
Counts
4 → 43
Calls

4 calls:

113.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
96.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
42.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 2627 to 1804 computations (31.3% saved)

simplify201.0ms (1.4%)

Algorithm
egg-herbie
Rules
658×associate-/l*_binary64
510×associate-/r*_binary64
334×cancel-sign-sub-inv_binary64
196×associate-/r/_binary64
185×distribute-rgt-neg-in_binary64
Counts
177 → 97
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02514942
16104519
219864371
348334371
449804371
549514371

prune114.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New91697
Fresh8614
Picked011
Done000
Total9913112
Error
1.2b
Counts
112 → 13
Alt Table
StatusErrorProgram
38.9b
(*.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)))))
37.2b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 4) (pow.f64 (sin.f64 ky) 4))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.9b
(*.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))))))
3.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
47.4b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))))
5.0b
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
47.4b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
3.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
48.2b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
44.2b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
34.0b
(*.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))))
7.4b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))))
37.3b
(*.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)))))
Compiler

Compiled 2056 to 1209 computations (41.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite242.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
1.2b
Rules
46×*-un-lft-identity_binary64
30×sqrt-prod_binary64 cbrt-prod_binary64
25×add-sqr-sqrt_binary64
24×times-frac_binary64
22×add-cube-cbrt_binary64
Counts
4 → 90
Calls

4 calls:

11.0ms
(cbrt.f64 (/.f64 (sin.f64 ky) (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)))
8.0ms
(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 4689 to 2789 computations (40.5% saved)

series317.0ms (2.2%)

Error
1.2b
Counts
4 → 38
Calls

4 calls:

113.0ms
(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
55.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
54.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
53.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Compiler

Compiled 4806 to 3101 computations (35.5% saved)

simplify157.0ms (1.1%)

Algorithm
egg-herbie
Rules
602×cancel-sign-sub-inv_binary64
371×associate-/l/_binary64
333×neg-mul-1_binary64
295×distribute-rgt-neg-in_binary64
279×distribute-lft-neg-in_binary64
Counts
128 → 65
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01573480
13063393
27383333
324123333
447233333
550293333

prune115.0ms (0.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New65065
Fresh01111
Picked011
Done011
Total651378
Error
1.2b
Counts
78 → 13
Alt Table
StatusErrorProgram
38.9b
(*.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)))))
37.2b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 4) (pow.f64 (sin.f64 ky) 4))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.9b
(*.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))))))
3.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
47.4b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))))
5.0b
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
47.4b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
3.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
48.2b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
44.2b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
34.0b
(*.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))))
7.4b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))))
37.3b
(*.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)))))
Compiler

Compiled 3135 to 1874 computations (40.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b
(/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.5b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.5b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite336.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
1.2b
Rules
96×*-un-lft-identity_binary64
72×times-frac_binary64
64×add-sqr-sqrt_binary64
56×add-cube-cbrt_binary64
54×cbrt-prod_binary64
Counts
4 → 160
Calls

4 calls:

14.0ms
(/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
13.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
8.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
Compiler

Compiled 6379 to 3852 computations (39.6% saved)

series386.0ms (2.6%)

Error
1.2b
Counts
4 → 39
Calls

4 calls:

139.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
78.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
77.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
46.0ms
(/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
Compiler

Compiled 3716 to 2709 computations (27.1% saved)

simplify223.0ms (1.5%)

Algorithm
egg-herbie
Rules
584×distribute-rgt-neg-in_binary64
574×associate-*l*_binary64
540×associate-*r*_binary64
293×cancel-sign-sub-inv_binary64
223×associate-/r*_binary64
Counts
199 → 189
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02847126
15706466
214276297
343016267
454226267

prune231.0ms (1.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New1872189
Fresh1910
Picked011
Done022
Total18814202
Error
1.2b
Counts
202 → 14
Alt Table
StatusErrorProgram
38.9b
(*.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)))))
37.2b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 4) (pow.f64 (sin.f64 ky) 4))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.9b
(*.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))))))
3.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
47.4b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))))
10.0b
(*.f64 (/.f64 (sin.f64 ky) (fabs.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 (sin.f64 kx) 4) (pow.f64 (sin.f64 ky) 4))) (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))))))
4.3b
(*.f64 (/.f64 (sin.f64 ky) (fabs.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (cbrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))) (cbrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))) (/.f64 (sin.f64 th) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
5.0b
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
47.4b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (*.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
3.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
48.2b
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
44.2b
(*.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (*.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
34.0b
(*.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))))
7.4b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))))
Compiler

Compiled 5486 to 3357 computations (38.8% saved)

regimes4.1s (27.8%)

Accuracy

Total 2.2b remaining (54.9%)

Threshold costs 0b (0%)

Compiler

Compiled 72984 to 51613 computations (29.3% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
11626
21626

end1.0ms (0%)

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample5.4s (36.6%)

Algorithm
intervals
Results
3.4s4629×body1024valid
661.0ms1411×body512valid
358.0ms514×body256valid
179.0ms1433×body128valid
16.0ms13×body2048valid
Compiler

Compiled 434 to 303 computations (30.2% saved)

Profiling

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