Details

Time bar (total: 5.5s)

analyze373.0ms (6.8%)

Algorithm
1×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)

sample37.0ms (0.7%)

Algorithm
1×intervals
Results
9.0ms197×body128valid
5.0ms19×body4096valid
5.0ms22×body2048valid
3.0ms256×pre128true
2.0ms10×body1024valid
1.0ms4×body512valid
0.0ms4×body256valid
Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify27.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
51×distribute-rgt-in_binary64
42×cancel-sign-sub-inv_binary64
37×sub-neg_binary64
27×neg-mul-1_binary64 unsub-neg_binary64
26×distribute-lft-in_binary64 associate--r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
11823
22923
34323
45723
58223
612223
716323
819023
921623
1022923
1123123
1224223
1325523
1426723
1528823
1628523
1728623
1824923

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
37.0b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶37.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
Compiler

Compiled 34 to 24 computations (29.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
1.0b
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
29.2b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite97.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Error
36.8b
Rules
10×add-sqr-sqrt_binary64
7×pow1_binary64 *-un-lft-identity_binary64
5×add-log-exp_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64
4×sqrt-div_binary64
3×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-pow1_binary64 cancel-sign-sub-inv_binary64
Counts
3 → 45
Calls

3 calls:

9.0ms
(sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
8.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
8.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 1063 to 371 computations (65.1% saved)

series109.0ms (2%)

Error
0.5b
Counts
3 → 33
Calls

3 calls:

31.0ms
(sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
31.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
29.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
Compiler

Compiled 1246 to 1022 computations (18% saved)

simplify98.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
530×cancel-sign-sub-inv_binary64
378×associate-*r*_binary64
359×associate-*l*_binary64
292×unswap-sqr_binary64
188×div-sub_binary64
Counts
78 → 40
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01341329
13061269
27471245
330131239
447321239
550391239

prune29.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New36440
Fresh000
Picked101
Done000
Total37441
Error
8.4b
Counts
41 → 4
Alt Table
StatusErrorProgram
44.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
55.5b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
43.6b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
▶34.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re))))
Compiler

Compiled 649 to 376 computations (42.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 1/2 (/.f64 (*.f64 re re) im))
0.0b
(-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re)
6.1b
(/.f64 (*.f64 re re) im)
13.8b
(sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re)))

rewrite118.0ms (2.1%)

Algorithm
1×rewrite-expression-head
Error
6.8b
Rules
18×add-exp-log_binary64 add-cbrt-cube_binary64
16×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
9×pow1_binary64 add-log-exp_binary64
Counts
4 → 80
Calls

4 calls:

7.0ms
(*.f64 1/2 (/.f64 (*.f64 re re) im))
7.0ms
(sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
6.0ms
(-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re)
5.0ms
(/.f64 (*.f64 re re) im)
Compiler

Compiled 1853 to 1014 computations (45.3% saved)

series129.0ms (2.3%)

Error
7.1b
Counts
4 → 39
Calls

4 calls:

43.0ms
(-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re)
34.0ms
(sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
23.0ms
(*.f64 1/2 (/.f64 (*.f64 re re) im))
19.0ms
(/.f64 (*.f64 re re) im)
Compiler

Compiled 1353 to 1099 computations (18.8% saved)

simplify116.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
465×times-frac_binary64
457×associate-/l*_binary64
383×associate-*l/_binary64
346×associate-*r/_binary64
273×distribute-lft-in_binary64
Counts
119 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01651909
13591741
211251716
346421716
449331716
550221716

prune45.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New73376
Fresh033
Picked101
Done000
Total74680
Error
6.7b
Counts
80 → 6
Alt Table
StatusErrorProgram
44.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
55.5b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
43.6b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (*.f64 re (/.f64 re im)))) re))))
32.6b
(*.f64 1/2 (-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im)) (*.f64 1/2 (*.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))))
▶32.2b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
Compiler

Compiled 1094 to 697 computations (36.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.4b
(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite35.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Error
6.7b
Rules
15×add-sqr-sqrt_binary64
10×sqrt-prod_binary64
6×associate-*l*_binary64 associate-*r*_binary64
5×pow1_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
4×unswap-sqr_binary64
Counts
1 → 31
Calls

1 calls:

7.0ms
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
Compiler

Compiled 294 to 220 computations (25.2% saved)

series9.0ms (0.2%)

Error
6.7b
Counts
1 → 3
Calls

1 calls:

9.0ms
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
Compiler

Compiled 81 to 73 computations (9.9% saved)

simplify92.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
564×log-div_binary64
359×associate-*l*_binary64
346×log-prod_binary64
296×associate-*l/_binary64
288×unswap-sqr_binary64
Counts
34 → 13
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
046367
183361
2199361
3249361
4342361
5528361
61013361
72695361
84284361
94989361
104907361

prune21.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New12113
Fresh055
Picked101
Done000
Total13619
Error
6.7b
Counts
19 → 6
Alt Table
StatusErrorProgram
44.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
▶32.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))))
55.5b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
43.6b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (*.f64 re (/.f64 re im)))) re))))
32.6b
(*.f64 1/2 (-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im)) (*.f64 1/2 (*.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))))
Compiler

Compiled 303 to 244 computations (19.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2))))
0.3b
(*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))

rewrite81.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
6.7b
Rules
38×add-sqr-sqrt_binary64
35×sqrt-prod_binary64
16×rem-sqrt-square_binary64
15×associate-*l*_binary64
14×pow1_binary64
Counts
2 → 68
Calls

2 calls:

12.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2))))
9.0ms
(*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))
Compiler

Compiled 904 to 762 computations (15.7% saved)

series20.0ms (0.4%)

Error
6.7b
Counts
2 → 6
Calls

2 calls:

10.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2))))
9.0ms
(*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))
Compiler

Compiled 193 to 177 computations (8.3% saved)

simplify97.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
427×cube-div_binary64
421×log-div_binary64
354×associate-*l*_binary64
346×associate-*l/_binary64
302×log-prod_binary64
Counts
74 → 48
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0731131
1140902
2369881
3638881
4723881
5943881
62299881
73776881
84960881

prune42.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New44448
Fresh055
Picked101
Done000
Total45954
Error
6.7b
Counts
54 → 9
Alt Table
StatusErrorProgram
44.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
34.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (exp.f64 (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))))
55.5b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
32.6b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 im)) (cbrt.f64 (sqrt.f64 im))) (*.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 im))))))
43.6b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
32.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))) (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)))) (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))))
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (*.f64 re (/.f64 re im)))) re))))
33.0b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)) (cbrt.f64 (sqrt.f64 (sqrt.f64 2))))))
32.6b
(*.f64 1/2 (-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im)) (*.f64 1/2 (*.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))))
Compiler

Compiled 655 to 537 computations (18% saved)

regimes2.4s (43.9%)

Accuracy

Total 7.1b remaining (50%)

Threshold costs 0b (0%)

Compiler

Compiled 18519 to 14039 computations (24.2% saved)

bsearch72.0ms (1.3%)

Steps
ItersRangePoint
9
3.304196338394284e+71
1.1495116378088179e+79
1.046298439081692e+72
10
-3.6106193883148243e-158
-2.1124676646818731e-168
-1.5807700503779843e-167
8
-1.1512110941409548e+66
-6.669116555704888e+62
-1.1335297314644595e+66
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
15×*-commutative_binary64
5×+-commutative_binary64
3×sub-neg_binary64
1×1-exp_binary64 neg-mul-1_binary64 neg-sub0_binary64 /-rgt-identity_binary64 *-lft-identity_binary64 distribute-neg-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04799
16899
27499
37699
47799
57699

end2.0ms (0%)

Compiler

Compiled 67 to 51 computations (23.9% saved)

sample1.4s (25.4%)

Algorithm
1×intervals
Results
286.0ms6024×body128valid
157.0ms542×body4096valid
147.0ms625×body2048valid
103.0ms8000×pre128true
94.0ms472×body1024valid
30.0ms229×body512valid
9.0ms108×body256valid
Compiler

Compiled 269 to 213 computations (20.8% saved)

Profiling

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