Details

Time bar (total: 10.7s)

analyze510.0ms (4.8%)

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
50%50%0.1%5
50%50%0.1%6
50%37.5%12.6%7
50%37.5%12.6%8
50%31.2%18.8%9
50%31.2%18.8%10
50%28.1%22%11
50%28.1%22%12
50%26.5%23.5%13
50%26.5%23.5%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample6.6s (61.3%)

Results
3.4s4992×body1024valid
1.1s2077×body1024invalid
708.0ms1728×body512valid
400.0ms432×body2048valid
365.0ms1008×body512invalid
189.0ms717×body256valid
142.0ms801×body128invalid
130.0ms517×body256invalid
67.0ms387×body128valid
1.0msbody2048invalid
Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify26.0ms (0.2%)

Algorithm
egg-herbie
Rules
623×associate-/l*_binary64
462×times-frac_binary64
358×fma-neg_binary64
346×fma-def_binary64
322×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01218
12318
25218
313218
428117
547317
692917
7237617
Stop Event
node limit
Counts
1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
57.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
57.6b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
Compiler

Compiled 53 to 38 computations (28.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 re)
0.0b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
6.0b
(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

series19.0ms (0.2%)

Counts
3 → 40
Calls

3 calls:

16.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms
(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
1.0ms
(cos.f64 re)

rewrite53.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
313×prod-diff_binary64
198×fma-def_binary64
178×expm1-udef_binary64
178×log1p-udef_binary64
152×log-pow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01231
125227
2336423
Stop Event
node limit
Counts
3 → 129
Calls

3 calls:

50.0ms
(cos.f64 re)
50.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
50.0ms
(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

simplify46.0ms (0.4%)

Algorithm
egg-herbie
Rules
611×fma-def_binary64
467×sub-neg_binary64
254×associate-*l*_binary64
242×associate-*r*_binary64
229×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0106809
1317787
21069754
34625754
Stop Event
node limit
Counts
169 → 164

prune80.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1631164
Fresh000
Picked011
Done000
Total1632165
Error
0.1b
Counts
165 → 2
Alt Table
StatusErrorProgram
57.6b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
1.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
Compiler

Compiled 3051 to 1713 computations (43.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))))
0.1b
(*.f64 (cos.f64 re) (pow.f64 im 3))
0.1b
(*.f64 (cos.f64 re) im)
0.1b
(*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))

series54.0ms (0.5%)

Counts
4 → 19
Calls

4 calls:

18.0ms
(+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))))
17.0ms
(*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))
13.0ms
(*.f64 (cos.f64 re) (pow.f64 im 3))
6.0ms
(*.f64 (cos.f64 re) im)

rewrite59.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
566×log-prod_binary64
372×fma-def_binary64
203×expm1-udef_binary64
203×log1p-udef_binary64
176×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01145
123645
2299045
Stop Event
node limit
Counts
4 → 119
Calls

4 calls:

57.0ms
(+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))))
57.0ms
(*.f64 (cos.f64 re) (pow.f64 im 3))
57.0ms
(*.f64 (cos.f64 re) im)
57.0ms
(*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))

simplify37.0ms (0.3%)

Algorithm
egg-herbie
Rules
611×fma-def_binary64
410×sub-neg_binary64
406×associate-*l*_binary64
378×cancel-sign-sub-inv_binary64
373×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
063488
1208455
2840391
34704391
Stop Event
node limit
Counts
138 → 152

prune136.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1448152
Fresh000
Picked011
Done011
Total14410154
Error
0.0b
Counts
154 → 10
Alt Table
StatusErrorProgram
2.6b
(neg.f64 (fma.f64 (pow.f64 (cbrt.f64 im) 2) (*.f64 (cbrt.f64 im) (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
29.3b
(neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 re) im) 2) (pow.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) 2)) (/.f64 1 (fma.f64 (cos.f64 re) im (*.f64 -1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))))
57.6b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
1.9b
(neg.f64 (fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
18.8b
(neg.f64 (fma.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (sqrt.f64 (cos.f64 re)) im) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
34.1b
(neg.f64 (fma.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
29.3b
(neg.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 re) im) 2) (pow.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) 2)) (fma.f64 (cos.f64 re) im (*.f64 -1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))))))
41.3b
(neg.f64 (/.f64 1 (/.f64 (fma.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) (-.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) (*.f64 (cos.f64 re) im)) (pow.f64 (*.f64 (cos.f64 re) im) 2)) (fma.f64 (pow.f64 (*.f64 (cos.f64 re) (pow.f64 im 3)) 3) 1/216 (pow.f64 (*.f64 (cos.f64 re) im) 3)))))
41.4b
(neg.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 (cos.f64 re) (pow.f64 im 3)) 3) 1/216 (pow.f64 (*.f64 (cos.f64 re) im) 3)) (/.f64 1 (fma.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) (-.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) (*.f64 (cos.f64 re) im)) (pow.f64 (*.f64 (cos.f64 re) im) 2)))))
1.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
Compiler

Compiled 3727 to 2226 computations (40.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (pow.f64 im 3) 1/6)
0.2b
(fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)))
0.3b
(pow.f64 (cbrt.f64 (cos.f64 re)) 2)
0.4b
(cbrt.f64 (cos.f64 re))

series686.0ms (6.4%)

Counts
4 → 60
Calls

4 calls:

439.0ms
(fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)))
127.0ms
(cbrt.f64 (cos.f64 re))
116.0ms
(pow.f64 (cbrt.f64 (cos.f64 re)) 2)
3.0ms
(*.f64 (pow.f64 im 3) 1/6)

rewrite53.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
611×log-prod_binary64
285×prod-diff_binary64
228×expm1-udef_binary64
228×log1p-udef_binary64
205×log-pow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01450
128640
2319538
Stop Event
node limit
Counts
4 → 92
Calls

4 calls:

51.0ms
(*.f64 (pow.f64 im 3) 1/6)
51.0ms
(fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)))
51.0ms
(pow.f64 (cbrt.f64 (cos.f64 re)) 2)
51.0ms
(cbrt.f64 (cos.f64 re))

simplify39.0ms (0.4%)

Algorithm
egg-herbie
Rules
420×fma-def_binary64
406×distribute-rgt-neg-in_binary64
350×sub-neg_binary64
316×associate-*l*_binary64
305×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
076804
1222800
2760689
33832689
Stop Event
node limit
Counts
152 → 120

prune184.0ms (1.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1495154
Fresh257
Picked101
Done022
Total15212164
Error
0.0b
Counts
164 → 12
Alt Table
StatusErrorProgram
2.6b
(neg.f64 (fma.f64 (pow.f64 (cbrt.f64 im) 2) (*.f64 (cbrt.f64 im) (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
29.3b
(neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 re) im) 2) (pow.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) 2)) (/.f64 1 (fma.f64 (cos.f64 re) im (*.f64 -1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))))
18.8b
(neg.f64 (fma.f64 (*.f64 im (pow.f64 (pow.f64 (cos.f64 re) 1/3) 2)) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
41.4b
(neg.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 (cos.f64 re) (pow.f64 im 3)) 3) 1/216 (pow.f64 (*.f64 (cos.f64 re) im) 3)) (/.f64 1 (fma.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) (-.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) (*.f64 (cos.f64 re) im)) (pow.f64 (*.f64 (cos.f64 re) im) 2)))))
57.6b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
1.9b
(neg.f64 (fma.f64 (*.f64 im (log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 (cos.f64 re)) 2))))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
2.0b
(neg.f64 (fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) 3) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
18.8b
(neg.f64 (fma.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (sqrt.f64 (cos.f64 re)) im) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
34.1b
(neg.f64 (fma.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
3.4b
(neg.f64 (fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))) (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))))) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
1.6b
(neg.f64 (fma.f64 (*.f64 im (cbrt.f64 (pow.f64 (cos.f64 re) 2))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
1.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
Compiler

Compiled 4304 to 2486 computations (42.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (*.f64 im (cbrt.f64 (pow.f64 (cos.f64 re) 2))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)))
0.3b
(pow.f64 (cos.f64 re) 2)
0.4b
(cbrt.f64 (pow.f64 (cos.f64 re) 2))
0.4b
(cbrt.f64 (cos.f64 re))

series597.0ms (5.6%)

Counts
3 → 40
Calls

3 calls:

421.0ms
(fma.f64 (*.f64 im (cbrt.f64 (pow.f64 (cos.f64 re) 2))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)))
173.0ms
(cbrt.f64 (pow.f64 (cos.f64 re) 2))
3.0ms
(pow.f64 (cos.f64 re) 2)

rewrite48.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
285×prod-diff_binary64
238×expm1-udef_binary64
238×log1p-udef_binary64
217×log-pow_binary64
139×add-sqr-sqrt_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01544
130334
2335232
Stop Event
node limit
Counts
3 → 73
Calls

3 calls:

47.0ms
(fma.f64 (*.f64 im (cbrt.f64 (pow.f64 (cos.f64 re) 2))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)))
47.0ms
(pow.f64 (cos.f64 re) 2)
47.0ms
(cbrt.f64 (pow.f64 (cos.f64 re) 2))

simplify36.0ms (0.3%)

Algorithm
egg-herbie
Rules
401×fma-def_binary64
379×distribute-rgt-neg-in_binary64
362×distribute-lft-neg-in_binary64
341×sub-neg_binary64
315×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
072677
1207667
2730558
33663558
Stop Event
node limit
Counts
113 → 100

prune158.0ms (1.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1313134
Fresh279
Picked101
Done022
Total13412146
Error
0.0b
Counts
146 → 12
Alt Table
StatusErrorProgram
2.6b
(neg.f64 (fma.f64 (pow.f64 (cbrt.f64 im) 2) (*.f64 (cbrt.f64 im) (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
29.3b
(neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 re) im) 2) (pow.f64 (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6)) 2)) (/.f64 1 (fma.f64 (cos.f64 re) im (*.f64 -1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))))
1.6b
(neg.f64 (fma.f64 (*.f64 im (cbrt.f64 (pow.f64 (cos.f64 re) 2))) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re)))) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
1.7b
(neg.f64 (fma.f64 (*.f64 im (cbrt.f64 (+.f64 1/2 (*.f64 1/2 (cos.f64 (+.f64 re re)))))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
1.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
57.6b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
1.9b
(neg.f64 (fma.f64 (*.f64 im (log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 (cos.f64 re)) 2))))) (cbrt.f64 (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
2.0b
(neg.f64 (fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) 3) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
18.8b
(neg.f64 (fma.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (sqrt.f64 (cos.f64 re)) im) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
34.1b
(neg.f64 (fma.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (cos.f64 re)) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
3.4b
(neg.f64 (fma.f64 (*.f64 im (pow.f64 (cbrt.f64 (cos.f64 re)) 2)) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))) (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))))) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
1.7b
(neg.f64 (fma.f64 (*.f64 im (cbrt.f64 (pow.f64 (cos.f64 re) 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (cos.f64 re)))))) (*.f64 (cos.f64 re) (*.f64 (pow.f64 im 3) 1/6))))
Compiler

Compiled 3455 to 2047 computations (40.8% saved)

regimes502.0ms (4.7%)

Accuracy

Total 0.5b remaining (89.7%)

Threshold costs 0.5b (89.7%)

Counts
73 → 2
Compiler

Compiled 8913 to 6153 computations (31% saved)

bsearch2.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
sub-neg_binary64
+-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02653
13953
24653
34953
45053
Stop Event
saturated

end774.0ms (7.2%)

Compiler

Compiled 366 to 234 computations (36.1% saved)

Profiling

Loading profile data...