Details

Time bar (total: 14.7s)

analyze1.8s (12%)

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)

sample308.0ms (2.1%)

Algorithm
intervals
Results
160.0ms149×body1024valid
27.0ms47×body512valid
9.0ms18×body256valid
7.0ms42×body128valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify85.0ms (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

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))
4.3b
(*.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 96 to 63 computations (34.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series386.0ms (2.6%)

Counts
3 → 84
Calls

3 calls:

209.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
148.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
29.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite14.0ms (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-*l*_binary64
Counts
3 → 73
Calls

3 calls:

7.0ms
(*.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 (0.7%)

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 → 182
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03244580
19034251
231454236
350434236

prune208.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New17012182
Fresh011
Picked101
Done000
Total17113184
Error
0b
Counts
184 → 13
Alt Table
StatusErrorProgram
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) 1) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
15.8b
(*.f64 (/.f64 (sin.f64 ky) (log.f64 (exp.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
3.1b
(*.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 (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
2.5b
(*.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)))
31.4b
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
1.3b
(*.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)))
6.3b
(*.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)))
0.4b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
4.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
25.0b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) 3))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
25.0b
(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))))
7.7b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))
Compiler

Compiled 5417 to 2098 computations (61.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.1b
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
0.2b
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

series390.0ms (2.7%)

Counts
3 → 84
Calls

3 calls:

208.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
131.0ms
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
52.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite38.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
156×times-frac_binary64
103×add-sqr-sqrt_binary64
91×*-un-lft-identity_binary64
89×add-cube-cbrt_binary64
44×associate-*l*_binary64
Counts
3 → 181
Calls

3 calls:

13.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
5.0ms
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
3.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

simplify183.0ms (1.2%)

Algorithm
egg-herbie
Rules
453×cancel-sign-sub-inv_binary64
256×associate-*r*_binary64
232×fma-def_binary64
219×sub-neg_binary64
203×*-commutative_binary64
Counts
265 → 344
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03697707
110017004
236716977
349596977

prune352.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New3752377
Fresh3912
Picked011
Done000
Total37812390
Error
0b
Counts
390 → 12
Alt Table
StatusErrorProgram
0.3b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) 1) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
15.8b
(*.f64 (/.f64 (sin.f64 ky) (log.f64 (exp.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
2.5b
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1)) (*.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th)))
25.0b
(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))))
1.3b
(*.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)))
6.3b
(*.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)))
0.4b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
4.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
25.0b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) 3))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
7.7b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))
Compiler

Compiled 10899 to 4018 computations (63.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series212.0ms (1.4%)

Counts
1 → 36
Calls

1 calls:

212.0ms
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
43×*-un-lft-identity_binary64
43×add-sqr-sqrt_binary64
43×add-cube-cbrt_binary64
13×associate-/r*_binary64
Counts
1 → 72
Calls

1 calls:

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

simplify125.0ms (0.9%)

Algorithm
egg-herbie
Rules
939×times-frac_binary64
436×fma-def_binary64
325×fma-neg_binary64
230×cancel-sign-sub-inv_binary64
162×neg-sub0_binary64
Counts
108 → 128
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02714113
16933975
223603911
345643898
450643898

prune199.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2252227
Fresh3710
Picked101
Done011
Total22910239
Error
0b
Counts
239 → 10
Alt Table
StatusErrorProgram
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) 1) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
15.8b
(*.f64 (/.f64 (sin.f64 ky) (log.f64 (exp.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.4b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
0.6b
(/.f64 1 (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
0.4b
(/.f64 (sin.f64 th) (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 ky)))
1.3b
(*.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)))
6.3b
(*.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)))
4.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
25.0b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) 3))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
Compiler

Compiled 6357 to 2091 computations (67.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.2b
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.3b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
0.3b
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

series542.0ms (3.7%)

Counts
3 → 96
Calls

3 calls:

217.0ms
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
204.0ms
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
121.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite21.0ms (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 → 95
Calls

3 calls:

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

simplify157.0ms (1.1%)

Algorithm
egg-herbie
Rules
505×cancel-sign-sub-inv_binary64
260×fma-neg_binary64
258×associate-*r*_binary64
224×times-frac_binary64
221×associate-/l*_binary64
Counts
191 → 194
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03245455
19195141
235895141
349795141
449695141

prune211.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2270227
Fresh088
Picked011
Done011
Total22710237
Error
0b
Counts
237 → 10
Alt Table
StatusErrorProgram
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) 1) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
15.8b
(*.f64 (/.f64 (sin.f64 ky) (log.f64 (exp.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.4b
(*.f64 (sin.f64 ky) (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
0.6b
(/.f64 1 (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
0.4b
(/.f64 (sin.f64 th) (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 ky)))
1.3b
(*.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)))
6.3b
(*.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)))
4.3b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
25.0b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) 3))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
Compiler

Compiled 6558 to 3060 computations (53.3% saved)

regimes2.1s (14.6%)

Accuracy

Total 0.2b remaining (90.5%)

Threshold costs 0.2b (90.5%)

Counts
187 → 1
Compiler

Compiled 35681 to 22153 computations (37.9% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-rgt-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)

sample7.2s (48.9%)

Algorithm
intervals
Results
5.2s4625×body1024valid
942.0ms1421×body512valid
247.0ms1381×body128valid
221.0ms555×body256valid
36.0ms18×body2048valid
Compiler

Compiled 222 to 150 computations (32.4% saved)

Profiling

Loading profile data...