Details

Time bar (total: 20.8s)

analyze1.6s (7.5%)

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
25%74.9%0.1%5
43.7%56.2%0.1%6
43.7%56.2%0.1%7
53%46.8%0.1%8
60.8%39%0.1%9
60.8%39%0.1%10
64.7%35.1%0.1%11
68.3%31.6%0.1%12
68.3%31.6%0.1%13
70%29.8%0.1%14
Compiler

Compiled 20 to 15 computations (25% saved)

sample7.3s (35%)

Results
5.5s4692×body1024valid
996.0ms1446×body512valid
382.0ms1540×body128valid
264.0ms566×body256valid
28.0ms12×body2048valid
Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify85.0ms (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

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))
5.6b
(*.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%)

Local error

Found 3 expressions with local error:

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

series373.0ms (1.8%)

Counts
3 → 84
Calls

3 calls:

206.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
132.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
35.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite13.0ms (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))

simplify148.0ms (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 → 184
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03244580
19034251
231454236
350434236

prune249.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1759184
Fresh101
Picked101
Done000
Total1779186
Error
0b
Counts
186 → 9
Alt Table
StatusErrorProgram
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))
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (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)))
9.3b
(*.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))
6.8b
(*.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)))
0.2b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(*.f64 (expm1.f64 (log1p.f64 (/.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 kx) (sin.f64 ky)))) (sin.f64 th))
1.3b
(*.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))
Compiler

Compiled 5322 to 2010 computations (62.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.6s (12.7%)

Counts
3 → 84
Calls

3 calls:

2.3s
(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
249.0ms
(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
141.0ms
(expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite7.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 42
Calls

3 calls:

3.0ms
(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
1.0ms
(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
0.0ms
(expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

simplify154.0ms (0.7%)

Algorithm
egg-herbie
Rules
863×fma-def_binary64
426×cancel-sign-sub-inv_binary64
288×neg-mul-1_binary64
288×fma-neg_binary64
212×sub-neg_binary64
Counts
126 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02684064
17733894
227323858
346133856
450003856
549603856

prune212.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1870187
Fresh088
Picked011
Done000
Total1879196
Error
0b
Counts
196 → 9
Alt Table
StatusErrorProgram
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))
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (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)))
9.3b
(*.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))
6.8b
(*.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)))
0.2b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(*.f64 (expm1.f64 (log1p.f64 (/.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 kx) (sin.f64 ky)))) (sin.f64 th))
1.3b
(*.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))
Compiler

Compiled 5843 to 2527 computations (56.8% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
0.1b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series474.0ms (2.3%)

Counts
3 → 84
Calls

3 calls:

282.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
135.0ms
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
57.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite39.0ms (0.2%)

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)))
2.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

simplify214.0ms (1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
03697761
110017004
236706977
349596977

prune417.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3743377
Fresh347
Picked011
Done011
Total3779386
Error
0b
Counts
386 → 9
Alt Table
StatusErrorProgram
0.2b
(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky))) (sin.f64 th))
1.3b
(*.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))
9.7b
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) 3))) (sin.f64 th))
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
6.8b
(*.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)))
0.2b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (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)))
0.5b
(*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1)) (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)))) (sin.f64 th))
Compiler

Compiled 10793 to 3941 computations (63.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series510.0ms (2.5%)

Counts
4 → 88
Calls

4 calls:

216.0ms
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky))) (sin.f64 th))
159.0ms
(/.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
127.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
7.0ms
(/.f64 1 (sin.f64 ky))

rewrite164.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
863×times-frac_binary64
435×add-sqr-sqrt_binary64
406×*-un-lft-identity_binary64
400×add-cube-cbrt_binary64
174×associate-*l*_binary64
Counts
4 → 516
Calls

4 calls:

63.0ms
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky))) (sin.f64 th))
9.0ms
(/.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
3.0ms
(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms
(/.f64 1 (sin.f64 ky))

simplify382.0ms (1.8%)

Algorithm
egg-herbie
Rules
436×cancel-sign-sub-inv_binary64
250×*-commutative_binary64
242×associate-*l/_binary64
231×associate-*r*_binary64
229×sub-neg_binary64
Counts
604 → 738
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044417721
1121515808
2403815688
3503415688

prune767.0ms (3.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New7362738
Fresh246
Picked011
Done022
Total7389747
Error
0b
Counts
747 → 9
Alt Table
StatusErrorProgram
1.3b
(*.f64 (/.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))))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 1 (sin.f64 ky))) (sin.f64 th))
0.2b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky))) (sin.f64 th))
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (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)))
0.5b
(*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1)) (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)))) (sin.f64 th))
9.7b
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) 3))) (sin.f64 th))
0.4b
(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
Compiler

Compiled 23448 to 10472 computations (55.3% saved)

regimes4.9s (23.7%)

Accuracy

Total 0.2b remaining (80.8%)

Threshold costs 0.2b (80.8%)

Counts
419 → 1
Compiler

Compiled 88660 to 56516 computations (36.3% 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

end136.0ms (0.7%)

Compiler

Compiled 232 to 135 computations (41.8% saved)

Profiling

Loading profile data...