Details

Time bar (total: 14.3s)

analyze1.7s (11.7%)

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)

sample284.0ms (2%)

Algorithm
intervals
Results
143.0ms136×body1024valid
29.0ms47×body512valid
9.0ms55×body128valid
6.0ms18×body256valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify81.0ms (0.6%)

Algorithm
egg-herbie
Rules
645×associate-/r*_binary64
634×sqr-pow_binary64
394×associate-*l*_binary64
373×cube-prod_binary64
368×*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01426
12618
24018
36818
414118
534818
6105518
7179618
8248418
9269718
10296818
11331118
12370518
13460318
14479918

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Compiler

Compiled 58 to 35 computations (39.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.2b
(*.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)))

series351.0ms (2.5%)

Counts
3 → 84
Calls

3 calls:

192.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
128.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
32.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
19×times-frac_binary64
19×add-cube-cbrt_binary64
13×associate-*l*_binary64
Counts
3 → 73
Calls

3 calls:

5.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
3.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify110.0ms (0.8%)

Algorithm
egg-herbie
Rules
894×fma-def_binary64
479×cancel-sign-sub-inv_binary64
212×sub-neg_binary64
168×fma-neg_binary64
164×*-commutative_binary64
Counts
157 → 184
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03244580
19034251
231454236
350434236

prune167.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1768184
Fresh000
Picked101
Done000
Total1778185
Error
0b
Counts
185 → 8
Alt Table
StatusErrorProgram
8.7b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.4b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (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))
1.2b
(*.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
5.2b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 th) (sin.f64 ky)))
3.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Compiler

Compiled 5236 to 1982 computations (62.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
0.2b
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

series339.0ms (2.4%)

Counts
3 → 84
Calls

3 calls:

196.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
116.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
27.0ms
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
19×times-frac_binary64
19×add-cube-cbrt_binary64
13×associate-*l*_binary64
Counts
3 → 73
Calls

3 calls:

7.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
3.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.0ms
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify103.0ms (0.7%)

Algorithm
egg-herbie
Rules
894×fma-def_binary64
479×cancel-sign-sub-inv_binary64
212×sub-neg_binary64
168×fma-neg_binary64
164×*-commutative_binary64
Counts
157 → 154
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03244580
19034251
231454236
350434236

prune132.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1540154
Fresh077
Picked011
Done000
Total1548162
Error
0b
Counts
162 → 8
Alt Table
StatusErrorProgram
8.7b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.4b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (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))
1.2b
(*.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
5.2b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 th) (sin.f64 ky)))
3.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Compiler

Compiled 4627 to 1865 computations (59.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.2b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.2b
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.3b
(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series452.0ms (3.2%)

Counts
3 → 84
Calls

3 calls:

193.0ms
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
140.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
119.0ms
(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
31×add-exp-log_binary64
27×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
20×times-frac_binary64
20×add-cube-cbrt_binary64
Counts
3 → 97
Calls

3 calls:

7.0ms
(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
6.0ms
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
2.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify254.0ms (1.8%)

Algorithm
egg-herbie
Rules
427×cancel-sign-sub-inv_binary64
281×fma-neg_binary64
222×associate-*r*_binary64
214×sub-neg_binary64
196×fma-def_binary64
Counts
181 → 184
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03224957
19014637
232964637
349014633
449964633
549974633
649974633
749594633

prune209.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2170217
Fresh066
Picked011
Done011
Total2178225
Error
0b
Counts
225 → 8
Alt Table
StatusErrorProgram
8.7b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.4b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (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))
1.2b
(*.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
5.2b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 th) (sin.f64 ky)))
3.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Compiler

Compiled 6215 to 2887 computations (53.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.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))
0.2b
(/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
0.4b
(*.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)))))
0.4b
(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series603.0ms (4.2%)

Counts
4 → 108
Calls

4 calls:

193.0ms
(*.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))
150.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
133.0ms
(/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
126.0ms
(*.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)))))

rewrite57.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt_binary64
94×times-frac_binary64
67×*-un-lft-identity_binary64
64×add-exp-log_binary64
61×add-cube-cbrt_binary64
Counts
4 → 206
Calls

4 calls:

15.0ms
(*.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)))))
10.0ms
(*.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))
3.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
3.0ms
(/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify242.0ms (1.7%)

Algorithm
egg-herbie
Rules
405×associate-*r*_binary64
324×associate-*l*_binary64
311×fma-def_binary64
294×fma-neg_binary64
198×associate-/l*_binary64
Counts
314 → 323
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048710948
113399179
248219179
350559179

prune905.0ms (6.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3221323
Fresh145
Picked011
Done022
Total3238331
Error
0b
Counts
331 → 8
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.4b
(/.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky)) (sin.f64 th)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
8.7b
(*.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (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))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
5.2b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 th) (sin.f64 ky)))
3.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Compiler

Compiled 11562 to 3994 computations (65.5% saved)

regimes1.4s (9.7%)

Accuracy

Total 0.2b remaining (84.3%)

Threshold costs 0.2b (84.3%)

Counts
146 → 1
Compiler

Compiled 28090 to 16567 computations (41% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
11618
21518

end0.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample6.8s (47.9%)

Algorithm
intervals
Results
5.0s4670×body1024valid
890.0ms1392×body512valid
232.0ms1413×body128valid
221.0ms512×body256valid
25.0ms13×body2048valid
Compiler

Compiled 214 to 124 computations (42.1% saved)

Profiling

Loading profile data...