Details

Time bar (total: 5.0s)

analyze496.0ms (10%)

Algorithm
search
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
25%25%50%2
25%25%50%3
31.2%18.7%50%4
31.2%18.7%50%5
34.3%15.6%50%6
34.3%15.6%50%7
35.9%14%50%8
35.9%14%50%9
36.7%13.3%50%10
36.7%13.3%50%11
37.1%12.9%50%12
37.1%12.9%50%13
37.3%12.7%50%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample47.0ms (0.9%)

Algorithm
intervals
Results
12.0ms195×body128valid
6.0ms21×body2048valid
6.0ms16×body4096valid
5.0ms256×pre128true
3.0ms14×body1024valid
1.0msbody512valid
1.0msbody256valid
Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify29.0ms (0.6%)

Algorithm
egg-herbie
Rules
203×fma-def_binary64
142×fma-neg_binary64
51×distribute-rgt-in_binary64
42×cancel-sign-sub-inv_binary64
28×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01315
12015
23315
35015
46915
59815
615115
721115
826315
930515
1034315
1137915
1239615
1341515
1442815
1546515
1647715
1748615
1844915

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.0b
(hypot.f64 re im)
1.0b
(-.f64 (hypot.f64 re im) re)

series76.0ms (1.5%)

Counts
3 → 56
Calls

3 calls:

48.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
15.0ms
(hypot.f64 re im)
13.0ms
(-.f64 (hypot.f64 re im) re)

rewrite13.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
prod-diff_binary64
pow1_binary64
Counts
3 → 55
Calls

3 calls:

7.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
3.0ms
(-.f64 (hypot.f64 re im) re)
0.0ms
(hypot.f64 re im)

simplify119.0ms (2.4%)

Algorithm
egg-herbie
Rules
994×fma-neg_binary64
747×times-frac_binary64
413×cancel-sign-sub-inv_binary64
173×fma-def_binary64
158×sub-neg_binary64
Counts
111 → 136
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02382332
16112069
220781999
344661989
450151989

prune81.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1333136
Fresh000
Picked011
Done000
Total1334137
Error
0.3b
Counts
137 → 4
Alt Table
StatusErrorProgram
47.5b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
56.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
50.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
Compiler

Compiled 3269 to 2118 computations (35.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 re))
0.1b
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
0.4b
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im))
0.5b
(*.f64 (sqrt.f64 2) im)

series43.0ms (0.9%)

Counts
4 → 0
Calls

4 calls:

27.0ms
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
6.0ms
(sqrt.f64 (/.f64 1 re))
6.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im))
3.0ms
(*.f64 (sqrt.f64 2) im)

rewrite30.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod_binary64
32×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
22×pow1_binary64
Counts
4 → 114
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
6.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im))
4.0ms
(*.f64 (sqrt.f64 2) im)
2.0ms
(sqrt.f64 (/.f64 1 re))

simplify106.0ms (2.1%)

Algorithm
egg-herbie
Rules
468×associate-/l*_binary64
420×*-commutative_binary64
403×unswap-sqr_binary64
271×sqr-pow_binary64
214×associate-*l*_binary64
Counts
114 → 143
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01211600
12391498
27891498
312861498
426201498
530601498
644731498
750121498

prune136.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1358143
Fresh022
Picked101
Done011
Total13611147
Error
0.1b
Counts
147 → 11
Alt Table
StatusErrorProgram
47.5b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 (sqrt.f64 re)))) (sqrt.f64 (/.f64 1 (sqrt.f64 re)))))
47.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
47.4b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))
47.6b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))) (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
47.4b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)))) (sqrt.f64 (/.f64 1 re))))
50.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
56.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
47.5b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) im) (sqrt.f64 1/2)) (fabs.f64 (cbrt.f64 (/.f64 1 re)))) (sqrt.f64 (cbrt.f64 (/.f64 1 re)))))
47.7b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) im)))) (sqrt.f64 (/.f64 1 re))))
47.5b
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 2) im) (sqrt.f64 (/.f64 1 re)))))
Compiler

Compiled 3436 to 2897 computations (15.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))
0.2b
(*.f64 (sqrt.f64 (sqrt.f64 2)) im)
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))
0.4b
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)))

series43.0ms (0.9%)

Counts
4 → 36
Calls

4 calls:

27.0ms
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))
8.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)))
5.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) im)
3.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))

rewrite49.0ms (1%)

Algorithm
rewrite-expression-head
Rules
37×sqrt-prod_binary64
34×add-cbrt-cube_binary64
34×add-exp-log_binary64
34×pow1_binary64
27×add-sqr-sqrt_binary64
Counts
4 → 120
Calls

4 calls:

17.0ms
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))
11.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)))
8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))
5.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) im)

simplify105.0ms (2.1%)

Algorithm
egg-herbie
Rules
746×associate-/l*_binary64
609×*-commutative_binary64
357×associate-/r*_binary64
331×associate-*l*_binary64
320×unswap-sqr_binary64
Counts
156 → 166
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01402349
13012120
211332120
319392120
443462120
552052120

prune128.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1624166
Fresh549
Picked101
Done011
Total1689177
Error
0.1b
Counts
177 → 9
Alt Table
StatusErrorProgram
48.6b
(*.f64 1/2 (*.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 1/2)) (+.f64 (log.f64 (sqrt.f64 (sqrt.f64 2))) (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) im))))) (sqrt.f64 (/.f64 1 re))))
50.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
47.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
47.4b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
47.4b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)))) (sqrt.f64 (/.f64 1 re))))
47.4b
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re)))))
47.4b
(*.f64 1/2 (/.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 1)) (sqrt.f64 re)))
47.7b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) im)))) (sqrt.f64 (/.f64 1 re))))
Compiler

Compiled 4571 to 4024 computations (12% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re)))
0.2b
(*.f64 (sqrt.f64 (sqrt.f64 2)) im)
0.2b
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re))))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))

series47.0ms (0.9%)

Counts
2 → 24
Calls

2 calls:

27.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re))))
20.0ms
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re)))

rewrite37.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
25×add-cbrt-cube_binary64
25×add-exp-log_binary64
25×pow1_binary64
17×associate-*r*_binary64
16×sqrt-prod_binary64
Counts
2 → 67
Calls

2 calls:

16.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re))))
14.0ms
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re)))

simplify81.0ms (1.6%)

Algorithm
egg-herbie
Rules
560×*-commutative_binary64
547×associate-/l*_binary64
403×associate-*l/_binary64
395×unswap-sqr_binary64
329×associate-*r/_binary64
Counts
91 → 93
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01081734
12491548
210061548
317691548
440571548
550451548

prune146.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1662168
Fresh257
Picked101
Done011
Total1698177
Error
0.1b
Counts
177 → 8
Alt Table
StatusErrorProgram
48.6b
(*.f64 1/2 (*.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 1/2)) (+.f64 (log.f64 (sqrt.f64 (sqrt.f64 2))) (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) im))))) (sqrt.f64 (/.f64 1 re))))
50.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
48.7b
(*.f64 1/2 (exp.f64 (+.f64 (log.f64 (sqrt.f64 1/2)) (+.f64 (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (log.f64 (sqrt.f64 (/.f64 1 re)))))))
47.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
47.4b
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) im) (sqrt.f64 (/.f64 1 re)))))
47.4b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
47.4b
(*.f64 1/2 (/.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 1)) (sqrt.f64 re)))
Compiler

Compiled 4425 to 3894 computations (12% saved)

regimes1.6s (31.2%)

Accuracy

Total 7.3b remaining (98%)

Threshold costs 0b (0%)

Counts
155 → 2
Compiler

Compiled 23607 to 20387 computations (13.6% saved)

bsearch28.0ms (0.6%)

Steps
ItersRangePoint
5
0.004508886918637681
0.009655523632920484
0.007479677862419169
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02552
13552
23952
34152
44252
54152

end1.0ms (0%)

Compiler

Compiled 35 to 29 computations (17.1% saved)

sample1.5s (30.9%)

Algorithm
intervals
Results
403.0ms6086×body128valid
200.0ms639×body2048valid
183.0ms481×body4096valid
127.0ms8000×pre128true
104.0ms417×body1024valid
45.0ms239×body512valid
17.0ms138×body256valid
Compiler

Compiled 244 to 201 computations (17.6% saved)

Profiling

Loading profile data...