Details

Time bar (total: 2.9s)

analyze7.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
0%50%50%2
0%50%50%3
37.5%12.5%50%4
43.7%6.2%50%5
46.9%3.1%50%6
48.4%1.6%50%7
49.2%0.8%50%8
49.6%0.4%50%9
49.8%0.2%50%10
49.9%0.1%50%11
49.9%0%50%12
50%0%50%13
50%0%50%14
Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.3s (43.6%)

Results
1.2s8256×body128valid
Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify55.0ms (1.9%)

Algorithm
egg-herbie
Rules
581×associate-/r*_binary64
510×distribute-rgt-in_binary64
489×distribute-lft-in_binary64
463×fma-neg_binary64
415×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01131
14026
218517
391513
4234013
5445513
6495813
7507713

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
47.8b
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
0.4b
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (*.f64 i i))
0.4b
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series6.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
2.0ms
(/.f64 1 (*.f64 i i))

rewrite17.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
35×times-frac_binary64
33×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
15×add-exp-log_binary64
Counts
2 → 85
Calls

2 calls:

9.0ms
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
4.0ms
(/.f64 1 (*.f64 i i))

simplify126.0ms (4.4%)

Algorithm
egg-herbie
Rules
484×cancel-sign-sub-inv_binary64
484×fma-neg_binary64
262×associate-/l/_binary64
260×unsub-neg_binary64
197×neg-mul-1_binary64
Counts
109 → 114
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01571670
13041577
27011474
318551474
442051414
548871414
649991414
748671414

prune98.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1104114
Fresh101
Picked101
Done000
Total1124116
Error
0b
Counts
116 → 4
Alt Table
StatusErrorProgram
34.1b
(*.f64 -1/4 (pow.f64 i 2))
0.1b
(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.4b
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
0.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))
Compiler

Compiled 1893 to 1432 computations (24.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 2 (/.f64 1 i))
0.0b
(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b
(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b
(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series10.0ms (0.3%)

Counts
4 → 39
Calls

4 calls:

3.0ms
(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
3.0ms
(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
2.0ms
(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
1.0ms
(+.f64 2 (/.f64 1 i))

rewrite57.0ms (2%)

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt_binary64
101×*-un-lft-identity_binary64
96×times-frac_binary64
49×add-cube-cbrt_binary64
30×associate-*r*_binary64
Counts
4 → 185
Calls

4 calls:

25.0ms
(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
7.0ms
(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
7.0ms
(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
5.0ms
(+.f64 2 (/.f64 1 i))

simplify133.0ms (4.6%)

Algorithm
egg-herbie
Rules
499×associate-/l*_binary64
456×fma-def_binary64
288×associate-/l/_binary64
277×fma-neg_binary64
200×associate-/r*_binary64
Counts
224 → 263
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02654371
17044054
220983932
346203930
450263930

prune232.0ms (8.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2621263
Fresh123
Picked101
Done000
Total2643267
Error
0b
Counts
267 → 3
Alt Table
StatusErrorProgram
34.1b
(*.f64 -1/4 (pow.f64 i 2))
0.1b
(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 2 (/.f64 1 i)))
0.4b
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
Compiler

Compiled 6243 to 5397 computations (13.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 2 (/.f64 1 i))
0.1b
(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 2 (/.f64 1 i)))
0.1b
(/.f64 1/4 (+.f64 2 (/.f64 1 i)))

series7.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 2 (/.f64 1 i)))
3.0ms
(/.f64 1/4 (+.f64 2 (/.f64 1 i)))

rewrite57.0ms (2%)

Algorithm
rewrite-expression-head
Rules
362×times-frac_binary64
296×*-un-lft-identity_binary64
269×add-sqr-sqrt_binary64
115×add-cube-cbrt_binary64
66×difference-of-squares_binary64
Counts
2 → 255
Calls

2 calls:

16.0ms
(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 2 (/.f64 1 i)))
6.0ms
(/.f64 1/4 (+.f64 2 (/.f64 1 i)))

simplify258.0ms (9%)

Algorithm
egg-herbie
Rules
501×associate-/r*_binary64
442×associate-/l/_binary64
380×fma-def_binary64
290×times-frac_binary64
273×distribute-rgt-in_binary64
Counts
279 → 247
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03129049
17888830
220298811
347478810
451578810

prune209.0ms (7.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2680268
Fresh022
Picked011
Done000
Total2683271
Error
0b
Counts
271 → 3
Alt Table
StatusErrorProgram
34.1b
(*.f64 -1/4 (pow.f64 i 2))
0.1b
(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 2 (/.f64 1 i)))
0.4b
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
Compiler

Compiled 7115 to 6084 computations (14.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.4b
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

series4.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

4.0ms
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

rewrite9.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
21×times-frac_binary64
13×add-cube-cbrt_binary64
12×difference-of-squares_binary64
Counts
1 → 47
Calls

1 calls:

5.0ms
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

simplify90.0ms (3.1%)

Algorithm
egg-herbie
Rules
490×fma-neg_binary64
422×cancel-sign-sub-inv_binary64
390×times-frac_binary64
288×associate-/l*_binary64
224×div-sub_binary64
Counts
59 → 74
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01371059
12741013
2620989
31604947
44381947
54877947
64896947

prune56.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New74074
Fresh011
Picked011
Done011
Total74377
Error
0b
Counts
77 → 3
Alt Table
StatusErrorProgram
34.1b
(*.f64 -1/4 (pow.f64 i 2))
0.1b
(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 2 (/.f64 1 i)))
0.4b
(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
Compiler

Compiled 1187 to 1027 computations (13.5% saved)

regimes99.0ms (3.5%)

Accuracy

Total 0.1b remaining (95.8%)

Threshold costs 0.1b (95.8%)

Counts
52 → 1
Compiler

Compiled 1588 to 1295 computations (18.5% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
distribute-neg-frac_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
11722
22322
32522
42622
52422

end57.0ms (2%)

Compiler

Compiled 60 to 52 computations (13.3% saved)

Profiling

Loading profile data...