Details

Time bar (total: 8.5s)

analyze607.0ms (7.2%)

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)

sample180.0ms (2.1%)

Algorithm
intervals
Results
83.0ms154×body1024valid
32.0ms74×body1024invalid
22.0ms60×body512valid
11.0ms13×body2048valid
9.0ms35×body512invalid
4.0ms21×body256valid
2.0ms15×body256invalid
2.0ms20×body128invalid
1.0msbody128valid
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify81.0ms (1%)

Algorithm
egg-herbie
Rules
626×associate-/l*_binary64
547×div-sub_binary64
534×unswap-sqr_binary64
468×sub-neg_binary64
462×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
12218
24918
310418
417418
530618
654318
7124118
8328218
9415018
10435418
11534018

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
58.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
58.2b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
Compiler

Compiled 39 to 30 computations (23.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(exp.f64 im)
0.0b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
5.1b
(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite104.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
58.1b
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
cancel-sign-sub-inv_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
3 → 57
Calls

3 calls:

8.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
8.0ms
(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
1.0ms
(exp.f64 im)
Compiler

Compiled 1038 to 353 computations (66% saved)

series49.0ms (0.6%)

Error
0.1b
Counts
3 → 22
Calls

3 calls:

22.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
8.0ms
(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
5.0ms
(exp.f64 im)
Compiler

Compiled 832 to 587 computations (29.4% saved)

simplify82.0ms (1%)

Algorithm
egg-herbie
Rules
800×times-frac_binary64
423×*-commutative_binary64
267×distribute-rgt-in_binary64
253×unsub-neg_binary64
221×distribute-lft-in_binary64
Counts
79 → 54
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01621450
14241261
213821230
332021230
449981230

prune26.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New51354
Fresh000
Picked101
Done000
Total52355
Error
0.1b
Counts
55 → 3
Alt Table
StatusErrorProgram
58.2b
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re))) 3))
58.2b
(*.f64 (*.f64 1/2 (cos.f64 re)) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
0.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120))))
Compiler

Compiled 701 to 355 computations (49.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (pow.f64 im 5) 1/120)
0.1b
(*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))
0.1b
(*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6))
0.2b
(*.f64 (cos.f64 re) -1/6)

rewrite111.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
26×add-exp-log_binary64
25×associate-*l*_binary64
23×add-sqr-sqrt_binary64
15×add-cbrt-cube_binary64
14×*-un-lft-identity_binary64
Counts
4 → 94
Calls

4 calls:

7.0ms
(*.f64 (cos.f64 re) -1/6)
5.0ms
(*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6))
4.0ms
(*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))
4.0ms
(*.f64 (pow.f64 im 5) 1/120)
Compiler

Compiled 2165 to 1421 computations (34.4% saved)

series79.0ms (0.9%)

Error
0.1b
Counts
4 → 24
Calls

4 calls:

37.0ms
(*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))
16.0ms
(*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6))
7.0ms
(*.f64 (pow.f64 im 5) 1/120)
5.0ms
(*.f64 (cos.f64 re) -1/6)
Compiler

Compiled 1303 to 934 computations (28.3% saved)

simplify107.0ms (1.3%)

Algorithm
egg-herbie
Rules
296×associate-*l*_binary64
294×associate-*r*_binary64
277×distribute-rgt-in_binary64
271×distribute-lft-in_binary64
271×sub-neg_binary64
Counts
118 → 87
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01931738
14511596
217921560
342221552
448251552
549291552

prune75.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New78987
Fresh022
Picked011
Done000
Total781290
Error
0.0b
Counts
90 → 12
Alt Table
StatusErrorProgram
31.1b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (-.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (*.f64 (*.f64 re re) (+.f64 (*.f64 1/2 im) (*.f64 1/240 (pow.f64 im 5))))))
58.2b
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re))) 3))
17.1b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (sqrt.f64 (cos.f64 re)))))
1.0b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
28.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (/.f64 (*.f64 (cos.f64 re) (+.f64 (*.f64 im im) (*.f64 (pow.f64 im 10) -1/14400))) (-.f64 im (*.f64 (pow.f64 im 5) 1/120))))
33.6b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (sqrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (sqrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))))))
1.9b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (cbrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))))) (cbrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))))))
39.8b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))) 3)))
58.2b
(*.f64 (*.f64 1/2 (cos.f64 re)) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
0.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120))))
32.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cos.f64 re) (sqrt.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (sqrt.f64 (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))))
1.8b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cos.f64 re) (*.f64 (cbrt.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5)))) (cbrt.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5)))))) (cbrt.f64 (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))))
Compiler

Compiled 2219 to 1497 computations (32.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
0.3b
(cbrt.f64 (cos.f64 re))
0.3b
(cbrt.f64 (cos.f64 re))
0.3b
(cbrt.f64 (cos.f64 re))

rewrite98.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
15×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
11×pow1_binary64
Counts
4 → 73
Calls

4 calls:

5.0ms
(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
1.0ms
(cbrt.f64 (cos.f64 re))
1.0ms
(cbrt.f64 (cos.f64 re))
1.0ms
(cbrt.f64 (cos.f64 re))
Compiler

Compiled 2294 to 1037 computations (54.8% saved)

series94.0ms (1.1%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

27.0ms
(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
14.0ms
(cbrt.f64 (cos.f64 re))
13.0ms
(cbrt.f64 (cos.f64 re))
13.0ms
(cbrt.f64 (cos.f64 re))
Compiler

Compiled 1724 to 1165 computations (32.4% saved)

simplify138.0ms (1.6%)

Algorithm
egg-herbie
Rules
723×log-prod_binary64
499×unswap-sqr_binary64
432×distribute-rgt-neg-in_binary64
388×cancel-sign-sub-inv_binary64
340×distribute-lft-neg-in_binary64
Counts
97 → 74
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0781048
1156978
2455956
31204938
42807778
54052778
64531778
74986778
84891778

prune63.0ms (0.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New72274
Fresh4610
Picked011
Done011
Total761086
Error
0.0b
Counts
86 → 10
Alt Table
StatusErrorProgram
0.8b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 2)) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
32.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cos.f64 re) (sqrt.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (sqrt.f64 (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))))
17.0b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (pow.f64 (cos.f64 re) 2/3) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
1.0b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
28.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (/.f64 (*.f64 (cos.f64 re) (+.f64 (*.f64 im im) (*.f64 (pow.f64 im 10) -1/14400))) (-.f64 im (*.f64 (pow.f64 im 5) 1/120))))
33.6b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (sqrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (sqrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))))))
39.8b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))) 3)))
58.2b
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re))) 3))
58.2b
(*.f64 (*.f64 1/2 (cos.f64 re)) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
0.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120))))
Compiler

Compiled 1730 to 1060 computations (38.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 re) -1/6)
0.3b
(pow.f64 (cos.f64 re) 2)
0.3b
(cbrt.f64 (pow.f64 (cos.f64 re) 2))
0.3b
(cbrt.f64 (cos.f64 re))

rewrite93.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
11×cbrt-prod_binary64
11×add-cube-cbrt_binary64
add-exp-log_binary64
Counts
4 → 63
Calls

4 calls:

3.0ms
(*.f64 (cos.f64 re) -1/6)
2.0ms
(pow.f64 (cos.f64 re) 2)
2.0ms
(cbrt.f64 (pow.f64 (cos.f64 re) 2))
1.0ms
(cbrt.f64 (cos.f64 re))
Compiler

Compiled 1861 to 1156 computations (37.9% saved)

series68.0ms (0.8%)

Error
0.0b
Counts
4 → 21
Calls

4 calls:

17.0ms
(cbrt.f64 (pow.f64 (cos.f64 re) 2))
13.0ms
(cbrt.f64 (cos.f64 re))
12.0ms
(pow.f64 (cos.f64 re) 2)
6.0ms
(*.f64 (cos.f64 re) -1/6)
Compiler

Compiled 1423 to 1037 computations (27.1% saved)

simplify91.0ms (1.1%)

Algorithm
egg-herbie
Rules
496×sqr-pow_binary64
379×cancel-sign-sub-inv_binary64
354×sub-neg_binary64
350×*-commutative_binary64
275×associate-+l+_binary64
Counts
84 → 49
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0120785
1234744
2729731
31703713
43018709
54202709
64777709

prune42.0ms (0.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New49049
Fresh077
Picked011
Done022
Total491059
Error
0.0b
Counts
59 → 10
Alt Table
StatusErrorProgram
0.8b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 2)) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
32.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cos.f64 re) (sqrt.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (sqrt.f64 (+.f64 im (*.f64 (pow.f64 im 5) 1/120)))))
17.0b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (pow.f64 (cos.f64 re) 2/3) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
1.0b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (+.f64 im (*.f64 1/120 (pow.f64 im 5))) (cbrt.f64 (cos.f64 re)))))
28.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (/.f64 (*.f64 (cos.f64 re) (+.f64 (*.f64 im im) (*.f64 (pow.f64 im 10) -1/14400))) (-.f64 im (*.f64 (pow.f64 im 5) 1/120))))
33.6b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (sqrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5))))) (sqrt.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))))))
39.8b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 re) (+.f64 im (*.f64 1/120 (pow.f64 im 5)))) 3)))
58.2b
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re))) 3))
58.2b
(*.f64 (*.f64 1/2 (cos.f64 re)) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
0.5b
(-.f64 (*.f64 (pow.f64 im 3) (*.f64 (cos.f64 re) -1/6)) (*.f64 (cos.f64 re) (+.f64 im (*.f64 (pow.f64 im 5) 1/120))))
Compiler

Compiled 1121 to 735 computations (34.4% saved)

regimes861.0ms (10.2%)

Accuracy

Total 0.7b remaining (85.6%)

Threshold costs 0.7b (85.6%)

Compiler

Compiled 21260 to 14592 computations (31.4% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01629
12629
23629
34629
46329
57029
67429
77529
87429

end1.0ms (0%)

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample5.4s (63.3%)

Algorithm
intervals
Results
2.4s4882×body1024valid
1.1s1986×body1024invalid
454.0ms1671×body512valid
323.0ms437×body2048valid
243.0ms1013×body512invalid
110.0ms647×body256valid
77.0ms512×body256invalid
57.0ms672×body128invalid
30.0ms363×body128valid
Compiler

Compiled 296 to 214 computations (27.7% saved)

Profiling

Loading profile data...