Details

Time bar (total: 15.3s)

analyze1.7s (11.1%)

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)

sample306.0ms (2%)

Algorithm
intervals
Results
167.0ms157×body1024valid
26.0ms40×body512valid
7.0ms44×body128valid
5.0ms15×body256valid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify87.0ms (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))
2.3b
(*.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
0.0b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(/.f64 (sin.f64 ky) (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))

series387.0ms (2.5%)

Counts
3 → 84
Calls

3 calls:

227.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
131.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
28.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite13.0ms (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:

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)))
0.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify101.0ms (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

prune186.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New17111182
Fresh101
Picked101
Done000
Total17311184
Error
0b
Counts
184 → 11
Alt Table
StatusErrorProgram
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
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
10.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 3)) (sin.f64 th))
33.1b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
5.3b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (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))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.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))))) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
2.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Compiler

Compiled 5281 to 2016 computations (61.8% saved)

localize13.0ms (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 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.7b
(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series1.8s (11.6%)

Counts
3 → 84
Calls

3 calls:

1.4s
(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
213.0ms
(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
124.0ms
(expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite5.0ms (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))
0.0ms
(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)))))

simplify135.0ms (0.9%)

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

prune201.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1870187
Fresh01010
Picked011
Done000
Total18711198
Error
0b
Counts
198 → 11
Alt Table
StatusErrorProgram
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
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
10.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 3)) (sin.f64 th))
33.1b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
5.3b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (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))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.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))))) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
2.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Compiler

Compiled 5833 to 2553 computations (56.2% 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 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.2b
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

series453.0ms (3%)

Counts
3 → 96
Calls

3 calls:

230.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
193.0ms
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
29.0ms
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite611.0ms (4%)

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:

6.0ms
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
3.0ms
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.0ms
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify200.0ms (1.3%)

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

prune143.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1461147
Fresh189
Picked101
Done011
Total14810158
Error
0b
Counts
158 → 10
Alt Table
StatusErrorProgram
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
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
10.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 3)) (sin.f64 th))
33.1b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
5.3b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (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))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
2.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
9.0b
(*.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
Compiler

Compiled 4718 to 2038 computations (56.8% 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 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (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 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series391.0ms (2.6%)

Counts
3 → 84
Calls

3 calls:

202.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
136.0ms
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
53.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite35.0ms (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:

10.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
4.0ms
(/.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))

simplify161.0ms (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

prune354.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3761377
Fresh178
Picked101
Done011
Total3789387
Error
0b
Counts
387 → 9
Alt Table
StatusErrorProgram
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
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.2b
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
10.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 3)) (sin.f64 th))
33.1b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
5.3b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (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))
2.0b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
9.0b
(*.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
Compiler

Compiled 10572 to 3821 computations (63.9% saved)

regimes1.2s (7.8%)

Accuracy

Total 0.2b remaining (85.6%)

Threshold costs 0.2b (85.6%)

Counts
124 → 1
Compiler

Compiled 23184 to 14257 computations (38.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11118
21118

end0.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample6.8s (44.6%)

Algorithm
intervals
Results
5.0s4655×body1024valid
918.0ms1421×body512valid
237.0ms1379×body128valid
193.0ms533×body256valid
22.0ms12×body2048valid
Compiler

Compiled 198 to 125 computations (36.9% saved)

Profiling

Loading profile data...