Details

Time bar (total: 12.5s)

analyze2.8s (22.3%)

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
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14
Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.6s (36.6%)

Results
2.5s2135×body1024valid
1.0s4569×body128valid
762.0ms1048×body512valid
231.0ms501×body256valid
6.0msbody2048valid
2.0msbody128invalid
Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify40.0ms (0.3%)

Algorithm
egg-herbie
Rules
1051×fma-def_binary64
599×rules-5-rev_binary64
419×rules-5_binary64
323×rules-20_binary64
257×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01837
12932
27332
319132
498432
5410632
6516332

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
9.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
9.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 96 to 76 computations (20.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
8.5b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series162.0ms (1.3%)

Counts
4 → 120
Calls

4 calls:

95.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
43.0ms
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
14.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
10.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

rewrite115.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
521×prod-diff_binary64
242×egg-rr
153×add-sqr-sqrt_binary64
142×add-log-exp_binary64
142×log1p-expm1-u_binary64
Counts
4 → 242
Calls

4 calls:

109.0ms
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
109.0ms
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
109.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
109.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671
136371
2435371
3538471
000
100

simplify84.0ms (0.7%)

Algorithm
egg-herbie
Rules
787×fma-neg_binary64
380×rules-21_binary64
358×rules-14-rev_binary64
256×fma-def_binary64
216×rules-15-rev_binary64
Counts
362 → 303
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01963233
15943086
228453074
353333074

prune373.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2967303
Fresh000
Picked011
Done000
Total2968304
Error
0.0b
Counts
304 → 8
Alt Table
StatusErrorProgram
22.1b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (neg.f64 (*.f64 0 (*.f64 -2 J)))) (fma.f64 0 (*.f64 -2 J) (*.f64 0 (*.f64 -2 J)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.7b
U
10.1b
(*.f64 (fma.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))) 2) (cbrt.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))) 0) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.4b
(neg.f64 U)
37.4b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
9.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
34.9b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.2b
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 12235 to 9549 computations (22% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
0.2b
(/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J)))
8.5b
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series148.0ms (1.2%)

Counts
2 → 60
Calls

2 calls:

137.0ms
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
11.0ms
(/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J)))

rewrite98.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
534×prod-diff_binary64
165×add-sqr-sqrt_binary64
153×add-log-exp_binary64
153×log1p-expm1-u_binary64
153×expm1-log1p-u_binary64
Counts
2 → 124
Calls

2 calls:

95.0ms
(/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J)))
95.0ms
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01744
139044
2470244
3573544
000
100

simplify70.0ms (0.6%)

Algorithm
egg-herbie
Rules
973×rules-13_binary64
748×fma-neg_binary64
698×rules-20_binary64
311×rules-21_binary64
251×rules-14-rev_binary64
Counts
184 → 170
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01772325
15112184
224442172
368372172

prune355.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2872289
Fresh246
Picked011
Done011
Total2898297
Error
0.0b
Counts
297 → 8
Alt Table
StatusErrorProgram
47.7b
U
22.1b
(*.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
10.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
37.4b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
9.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.4b
(neg.f64 U)
34.9b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.2b
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 11441 to 8948 computations (21.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2))
0.5b
(pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)
0.6b
(cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J)))
8.5b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series1.2s (9.3%)

Counts
4 → 108
Calls

4 calls:

488.0ms
(pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)
446.0ms
(cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J)))
151.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
76.0ms
(*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2))

rewrite153.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
679×prod-diff_binary64
316×egg-rr
172×add-sqr-sqrt_binary64
161×log1p-expm1-u_binary64
161×expm1-log1p-u_binary64
Counts
4 → 316
Calls

4 calls:

143.0ms
(*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2))
143.0ms
(pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)
143.0ms
(cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J)))
143.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01975
141573
2487473
3620273
000
100

simplify143.0ms (1.1%)

Algorithm
egg-herbie
Rules
863×fma-neg_binary64
396×rules-21_binary64
303×fma-def_binary64
236×rules-15-rev_binary64
232×rules-20_binary64
Counts
424 → 392
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02683641
17243460
233143360
350293360

prune552.0ms (4.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New4460446
Fresh055
Picked011
Done022
Total4468454
Error
0.0b
Counts
454 → 8
Alt Table
StatusErrorProgram
47.7b
U
22.1b
(*.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
10.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
37.4b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
9.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.4b
(neg.f64 U)
34.9b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.2b
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 21380 to 17022 computations (20.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))
0.1b
(*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))))
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
7.5b
(*.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series109.0ms (0.9%)

Counts
2 → 60
Calls

2 calls:

98.0ms
(*.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
11.0ms
(*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))))

rewrite120.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
629×prod-diff_binary64
171×add-sqr-sqrt_binary64
170×egg-rr
159×add-log-exp_binary64
159×log1p-expm1-u_binary64
Counts
2 → 170
Calls

2 calls:

114.0ms
(*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))))
114.0ms
(*.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01844
140944
2493244
3616844
000
100

simplify116.0ms (0.9%)

Algorithm
egg-herbie
Rules
973×rules-13_binary64
748×fma-neg_binary64
698×rules-20_binary64
311×rules-21_binary64
251×rules-14-rev_binary64
Counts
230 → 216
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01772325
15112184
224442172
368372172

prune487.0ms (3.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New3350335
Fresh044
Picked011
Done033
Total3358343
Error
0.0b
Counts
343 → 8
Alt Table
StatusErrorProgram
47.7b
U
22.1b
(*.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))) (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
10.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J))) 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
37.4b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
9.1b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.4b
(neg.f64 U)
34.9b
(*.f64 (-.f64 (*.f64 1/4 (*.f64 (pow.f64 K 2) J)) (*.f64 2 J)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.2b
(*.f64 (/.f64 (cos.f64 (/.f64 K 2)) (/.f64 1 (*.f64 -2 J))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
Compiler

Compiled 14999 to 11846 computations (21% saved)

regimes572.0ms (4.6%)

Accuracy

Total 9.3b remaining (99.7%)

Threshold costs 0b (0%)

Counts
59 → 2
Compiler

Compiled 9950 to 7890 computations (20.7% saved)

bsearch52.0ms (0.4%)

Steps
ItersRangePoint
5
1.8496974450358866e+172
7.358482293982686e+172
7.165885222303086e+172
Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02141
12341
22241

end149.0ms (1.2%)

Compiler

Compiled 241 to 191 computations (20.7% saved)

Profiling

Loading profile data...