Details

Time bar (total: 5.2s)

analyze461.0ms (8.9%)

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)

sample46.0ms (0.9%)

Algorithm
intervals
Results
13.0ms191×body128valid
8.0ms22×body4096valid
6.0ms21×body2048valid
4.0ms256×pre128true
3.0ms14×body1024valid
1.0msbody512valid
0.0msbody256valid
Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify32.0ms (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 → 1
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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
14.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 36 to 27 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(hypot.f64 re im)
0.0b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.4b
(-.f64 (hypot.f64 re im) re)

rewrite96.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
14.2b
Rules
26×add-cube-cbrt_binary64
16×add-sqr-sqrt_binary64
13×pow1_binary64
10×flip3--_binary64
10×add-log-exp_binary64
Counts
3 → 118
Calls

3 calls:

14.0ms
(-.f64 (hypot.f64 re im) re)
12.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
10.0ms
(hypot.f64 re im)
Compiler

Compiled 1977 to 797 computations (59.7% saved)

series81.0ms (1.6%)

Error
0.2b
Counts
3 → 40
Calls

3 calls:

28.0ms
(hypot.f64 re im)
21.0ms
(-.f64 (hypot.f64 re im) re)
17.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
Compiler

Compiled 1461 to 1193 computations (18.3% saved)

simplify67.0ms (1.3%)

Algorithm
egg-herbie
Rules
777×associate-*l*_binary64
484×fma-def_binary64
421×times-frac_binary64
280×associate-/l*_binary64
253×associate-/r*_binary64
Counts
158 → 66
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01881836
14331807
213231737
349101737

prune34.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New61566
Fresh000
Picked011
Done000
Total61667
Error
0.2b
Counts
67 → 6
Alt Table
StatusErrorProgram
15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re))))
14.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))))
46.5b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
56.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (*.f64 1/2 (/.f64 (*.f64 im im) re))))))
53.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
Compiler

Compiled 1136 to 662 computations (41.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
0.3b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
0.4b
(-.f64 (hypot.f64 re im) re)
0.4b
(-.f64 (hypot.f64 re im) re)

rewrite176.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
44×add-cube-cbrt_binary64
36×flip3--_binary64
31×sqrt-div_binary64
31×add-sqr-sqrt_binary64
20×pow1/2_binary64
Counts
4 → 193
Calls

4 calls:

18.0ms
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
18.0ms
(-.f64 (hypot.f64 re im) re)
15.0ms
(sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
15.0ms
(-.f64 (hypot.f64 re im) re)
Compiler

Compiled 5183 to 1479 computations (71.5% saved)

series102.0ms (2%)

Error
0.2b
Counts
4 → 54
Calls

4 calls:

22.0ms
(-.f64 (hypot.f64 re im) re)
21.0ms
(-.f64 (hypot.f64 re im) re)
21.0ms
(sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
21.0ms
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
Compiler

Compiled 2251 to 1708 computations (24.1% saved)

simplify155.0ms (3%)

Algorithm
egg-herbie
Rules
465×fma-def_binary64
420×times-frac_binary64
383×fma-neg_binary64
311×associate-/l*_binary64
248×cancel-sign-sub-inv_binary64
Counts
247 → 138
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02133111
14573022
214912887
344662874
449202874
549112874

prune58.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1380138
Fresh044
Picked011
Done011
Total1386144
Error
0.2b
Counts
144 → 6
Alt Table
StatusErrorProgram
15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re))))
14.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))))
46.5b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
56.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (*.f64 1/2 (/.f64 (*.f64 im im) re))))))
53.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
Compiler

Compiled 2636 to 1267 computations (51.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(hypot.f64 re im)
0.0b
(sqrt.f64 (*.f64 2 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
7.7b
(-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)

rewrite132.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
28×add-sqr-sqrt_binary64
27×add-cube-cbrt_binary64
21×pow1/2_binary64
15×pow1_binary64
14×add-cbrt-cube_binary64
Counts
4 → 170
Calls

4 calls:

17.0ms
(-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)
15.0ms
(sqrt.f64 (*.f64 2 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)))
14.0ms
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
11.0ms
(hypot.f64 re im)
Compiler

Compiled 3541 to 1142 computations (67.7% saved)

series99.0ms (1.9%)

Error
0.2b
Counts
4 → 56
Calls

4 calls:

24.0ms
(hypot.f64 re im)
21.0ms
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
20.0ms
(-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)
19.0ms
(sqrt.f64 (*.f64 2 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)))
Compiler

Compiled 2229 to 1758 computations (21.1% saved)

simplify135.0ms (2.6%)

Algorithm
egg-herbie
Rules
595×fma-neg_binary64
547×fma-def_binary64
421×times-frac_binary64
303×associate-/l*_binary64
266×associate-/r*_binary64
Counts
226 → 129
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02202412
14822309
214722248
343112238
448542238
549462238

prune54.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1272129
Fresh033
Picked101
Done112
Total1296135
Error
0.2b
Counts
135 → 6
Alt Table
StatusErrorProgram
15.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)) (*.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))))))
46.5b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
56.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (*.f64 1/2 (/.f64 (*.f64 im im) re))))))
53.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
16.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) re))))
Compiler

Compiled 2013 to 1096 computations (45.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b
(cbrt.f64 (-.f64 (hypot.f64 re im) re))
0.4b
(cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re))
0.5b
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
7.7b
(-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)

rewrite134.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
31×add-cube-cbrt_binary64
26×add-sqr-sqrt_binary64
15×pow1/2_binary64
15×flip3--_binary64
12×add-exp-log_binary64
Counts
4 → 168
Calls

4 calls:

17.0ms
(-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)
15.0ms
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
13.0ms
(cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re))
11.0ms
(cbrt.f64 (-.f64 (hypot.f64 re im) re))
Compiler

Compiled 5230 to 1245 computations (76.2% saved)

series145.0ms (2.8%)

Error
0.2b
Counts
4 → 59
Calls

4 calls:

37.0ms
(cbrt.f64 (-.f64 (hypot.f64 re im) re))
36.0ms
(cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re))
25.0ms
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
23.0ms
(-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)
Compiler

Compiled 4497 to 2837 computations (36.9% saved)

simplify148.0ms (2.9%)

Algorithm
egg-herbie
Rules
552×fma-def_binary64
530×times-frac_binary64
512×fma-neg_binary64
264×cancel-sign-sub-inv_binary64
192×unswap-sqr_binary64
Counts
227 → 136
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02482972
15362832
215502697
342212663
449422663
548882663

prune64.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1351136
Fresh044
Picked011
Done011
Total1357142
Error
0.2b
Counts
142 → 7
Alt Table
StatusErrorProgram
17.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)) (*.f64 (*.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/6) (pow.f64 (-.f64 (hypot.f64 re im) re) 1/6)) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))))))
46.5b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
15.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))) re)) (*.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
56.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (*.f64 1/2 (/.f64 (*.f64 im im) re))))))
53.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
16.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) re))))
Compiler

Compiled 3394 to 1192 computations (64.9% saved)

regimes1.4s (26.7%)

Accuracy

Total 7.7b remaining (96.8%)

Threshold costs 0b (0%)

Compiler

Compiled 21602 to 12942 computations (40.1% saved)

bsearch31.0ms (0.6%)

Steps
ItersRangePoint
7
2.3334077665329976e+27
6.607954113191062e+28
6.533938137062735e+28
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
*-lft-identity_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02443
13543
23943
34143
44243
54143

end1.0ms (0%)

Compiler

Compiled 30 to 24 computations (20% saved)

sample1.5s (29%)

Algorithm
intervals
Results
397.0ms6057×body128valid
205.0ms533×body4096valid
185.0ms616×body2048valid
120.0ms8000×pre128true
104.0ms443×body1024valid
39.0ms224×body512valid
15.0ms127×body256valid
Compiler

Compiled 214 to 143 computations (33.2% saved)

Profiling

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