Details

Time bar (total: 29.4s)

analyze3.3s (11.2%)

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)

sample436.0ms (1.5%)

Algorithm
intervals
Results
324.0ms148×body1024valid
63.0ms54×body512valid
12.0ms38×body128valid
12.0ms15×body256valid
3.0msbody2048valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify113.0ms (0.4%)

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

prune8.0ms (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
4.2b
(*.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
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Compiler

Compiled 96 to 63 computations (34.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 ky)
0.1b
(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)))

rewrite29.0ms (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:

12.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
5.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms
(sin.f64 ky)
1.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

series977.0ms (3.3%)

Counts
4 → 88
Calls

4 calls:

533.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
306.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
135.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms
(sin.f64 ky)

simplify469.0ms (1.6%)

Algorithm
egg-herbie
Rules
539×cancel-sign-sub-inv_binary64
308×fma-neg_binary64
224×sub-neg_binary64
206×fma-def_binary64
164×*-commutative_binary64
Counts
170 → 317
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03354685
19304356
232354356
348634352
449904352
549974352
649994352
749544352

prune410.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New30611317
Fresh101
Picked101
Done000
Total30811319
Error
0b
Counts
319 → 11
Alt Table
StatusErrorProgram
29.8b
(*.f64 (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
2.7b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
14.2b
(*.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (*.f64 (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
21.1b
(cbrt.f64 (*.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)))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 th)) (sin.f64 th))))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
1.2b
(*.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)))
1.2b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
5.7b
(*.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)))
1.2b
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
0.3b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
Compiler

Compiled 5658 to 2166 computations (61.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(log1p.f64 (expm1.f64 (sin.f64 ky)))
0.1b
(expm1.f64 (sin.f64 ky))
0.2b
(*.f64 (/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
0.2b
(/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite25.0ms (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 → 85
Calls

4 calls:

10.0ms
(*.f64 (/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
4.0ms
(/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms
(expm1.f64 (sin.f64 ky))
1.0ms
(log1p.f64 (expm1.f64 (sin.f64 ky)))

series3.3s (11.2%)

Counts
4 → 84
Calls

4 calls:

1.7s
(*.f64 (/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
1.2s
(/.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
447.0ms
(log1p.f64 (expm1.f64 (sin.f64 ky)))
5.0ms
(expm1.f64 (sin.f64 ky))

simplify254.0ms (0.9%)

Algorithm
egg-herbie
Rules
814×fma-def_binary64
448×cancel-sign-sub-inv_binary64
217×times-frac_binary64
196×fma-neg_binary64
187×sub-neg_binary64
Counts
169 → 317
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03074372
18574068
231554027
349944027
449694027

prune352.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3152317
Fresh3710
Picked101
Done000
Total3199328
Error
0b
Counts
328 → 9
Alt Table
StatusErrorProgram
1.2b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.3b
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
4.8b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
0.3b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
1.2b
(*.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)))
29.8b
(*.f64 (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.7b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
5.7b
(*.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)))
1.2b
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
Compiler

Compiled 5631 to 1951 computations (65.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
19×times-frac_binary64
18×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
13×associate-*r*_binary64
Counts
2 → 63
Calls

2 calls:

10.0ms
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
6.0ms
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series2.2s (7.5%)

Counts
2 → 72
Calls

2 calls:

1.8s
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
428.0ms
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify306.0ms (1%)

Algorithm
egg-herbie
Rules
763×fma-def_binary64
424×cancel-sign-sub-inv_binary64
242×times-frac_binary64
206×fma-neg_binary64
202×associate-*r*_binary64
Counts
135 → 218
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02754508
17914329
232174233
349254233
449964233
549594233

prune319.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2942296
Fresh358
Picked011
Done000
Total2978305
Error
0b
Counts
305 → 8
Alt Table
StatusErrorProgram
1.2b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.3b
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
2.8b
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
29.8b
(*.f64 (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.7b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.5b
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
1.2b
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
4.8b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
Compiler

Compiled 5411 to 1954 computations (63.9% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(expm1.f64 (sin.f64 ky))
0.3b
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
0.3b
(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
0.4b
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite180.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
526×times-frac_binary64
303×add-sqr-sqrt_binary64
279×*-un-lft-identity_binary64
279×add-cube-cbrt_binary64
269×sqrt-prod_binary64
Counts
3 → 382
Calls

3 calls:

61.0ms
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
17.0ms
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
6.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series2.8s (9.5%)

Counts
3 → 108
Calls

3 calls:

1.8s
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
545.0ms
(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
462.0ms
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify798.0ms (2.7%)

Algorithm
egg-herbie
Rules
574×fma-def_binary64
398×associate-*r*_binary64
334×associate-/l*_binary64
312×associate-*l*_binary64
302×associate-/l/_binary64
Counts
490 → 893
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
056719982
1154218600
2495718582
3528618582

prune726.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New9650965
Fresh066
Picked011
Done011
Total9658973
Error
0b
Counts
973 → 8
Alt Table
StatusErrorProgram
1.2b
(*.f64 (/.f64 (/.f64 (sin.f64 ky) (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
0.3b
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
2.8b
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
29.8b
(*.f64 (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.7b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.5b
(*.f64 (log1p.f64 (expm1.f64 (sin.f64 ky))) (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
1.2b
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
4.8b
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
Compiler

Compiled 21262 to 4097 computations (80.7% saved)

regimes3.9s (13.2%)

Accuracy

Total 0.2b remaining (83.4%)

Threshold costs 0.2b (83.4%)

Compiler

Compiled 38311 to 24092 computations (37.1% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
11618
21518

end1.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample8.4s (28.5%)

Algorithm
intervals
Results
6.1s4626×body1024valid
1.1s1474×body512valid
317.0ms1354×body128valid
251.0ms530×body256valid
37.0ms16×body2048valid
Compiler

Compiled 205 to 122 computations (40.5% saved)

Profiling

Loading profile data...