Details

Time bar (total: 16.8s)

analyze1.8s (10.9%)

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)

sample8.1s (48%)

Results
6.1s4833×body1024valid
1.1s1442×body512valid
376.0ms1470×body128valid
256.0ms499×body256valid
31.0ms12×body2048valid
Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify84.0ms (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
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

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
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
2.2b
(*.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 96 to 63 computations (34.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 kx)
0.0b
(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))
0.1b
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series350.0ms (2.1%)

Counts
4 → 88
Calls

4 calls:

193.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
126.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
29.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms
(sin.f64 kx)

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*l*_binary64
Counts
4 → 82
Calls

4 calls:

5.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
2.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms
(sin.f64 kx)
0.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify136.0ms (0.8%)

Algorithm
egg-herbie
Rules
539×cancel-sign-sub-inv_binary64
307×fma-neg_binary64
224×sub-neg_binary64
206×fma-def_binary64
167×*-commutative_binary64
Counts
170 → 200
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03434685
19474356
232704356
349154352
449904352

prune198.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1919200
Fresh101
Picked101
Done000
Total1939202
Error
0.0b
Counts
202 → 9
Alt Table
StatusErrorProgram
0.3b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
11.7b
(*.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))
18.1b
(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
1.4b
(*.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) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.5b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
4.7b
(*.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)))
1.3b
(*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
Compiler

Compiled 5543 to 2135 computations (61.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series1.0s (6.2%)

Counts
3 → 96
Calls

3 calls:

803.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
201.0ms
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
28.0ms
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite12.0ms (0.1%)

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

3 calls:

5.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
2.0ms
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.0ms
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify198.0ms (1.2%)

Algorithm
egg-herbie
Rules
555×cancel-sign-sub-inv_binary64
257×fma-neg_binary64
228×times-frac_binary64
214×sub-neg_binary64
201×associate-*r*_binary64
Counts
169 → 147
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03265096
19204768
235744768
349144768
449864768
550004768
649594768

prune174.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1612163
Fresh178
Picked101
Done000
Total1639172
Error
0b
Counts
172 → 9
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
11.7b
(*.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))
0.4b
(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
18.1b
(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
0.5b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
4.7b
(*.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)))
1.3b
(*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
Compiler

Compiled 5031 to 2165 computations (57% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(*.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))))

series503.0ms (3%)

Counts
3 → 84
Calls

3 calls:

240.0ms
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
136.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
126.0ms
(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite23.0ms (0.1%)

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)))

simplify220.0ms (1.3%)

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

prune222.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2161217
Fresh178
Picked011
Done000
Total2179226
Error
0b
Counts
226 → 9
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
11.7b
(*.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))
1.3b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.4b
(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
18.1b
(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
0.5b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
4.7b
(*.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)))
Compiler

Compiled 6246 to 2915 computations (53.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.1b
(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
0.1b
(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.3b
(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series1.4s (8.6%)

Counts
4 → 108
Calls

4 calls:

1.1s
(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
200.0ms
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
122.0ms
(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
32.0ms
(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*l*_binary64
Counts
4 → 85
Calls

4 calls:

5.0ms
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.0ms
(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
0.0ms
(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.0ms
(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify128.0ms (0.8%)

Algorithm
egg-herbie
Rules
295×sub-neg_binary64
278×fma-def_binary64
251×times-frac_binary64
238×associate-/r*_binary64
207×associate-/l*_binary64
Counts
193 → 221
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04225770
112085276
244665273
350325273

prune196.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2210221
Fresh077
Picked011
Done011
Total2219230
Error
0b
Counts
230 → 9
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
11.7b
(*.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))
1.3b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.4b
(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
18.1b
(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
0.5b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
4.7b
(*.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)))
Compiler

Compiled 6808 to 2695 computations (60.4% saved)

regimes1.7s (10.3%)

Accuracy

Total 0.2b remaining (88.1%)

Threshold costs 0.2b (88.1%)

Counts
178 → 1
Compiler

Compiled 32081 to 19331 computations (39.7% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11118
21118

end139.0ms (0.8%)

Compiler

Compiled 213 to 124 computations (41.8% saved)

Profiling

Loading profile data...