Details

Time bar (total: 5.3s)

analyze477.0ms (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)

sample47.0ms (0.9%)

Algorithm
intervals
Results
13.0ms195×body128valid
8.0ms29×body2048valid
6.0ms16×body4096valid
4.0ms256×pre128true
2.0msbody512valid
2.0msbody1024valid
0.0msbody256valid
Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify29.0ms (0.6%)

Algorithm
egg-herbie
Rules
51×distribute-rgt-in_binary64
42×cancel-sign-sub-inv_binary64
37×sub-neg_binary64
27×unsub-neg_binary64
27×neg-mul-1_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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
38.8b
Counts
1 → 1
Alt Table
StatusErrorProgram
38.8b
(*.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)))
0.1b
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
30.7b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite71.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
38.6b
Rules
10×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
pow1_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
Counts
3 → 45
Calls

3 calls:

8.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
7.0ms
(sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
3.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 1063 to 371 computations (65.1% saved)

series110.0ms (2.1%)

Error
0.2b
Counts
3 → 45
Calls

3 calls:

36.0ms
(sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))
31.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
23.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 1979 to 1639 computations (17.2% saved)

simplify65.0ms (1.2%)

Algorithm
egg-herbie
Rules
557×associate-*r*_binary64
496×associate-*l*_binary64
356×times-frac_binary64
306×associate-/l*_binary64
204×associate-/r*_binary64
Counts
90 → 54
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01851855
14551794
212431746
350891746

prune35.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New47754
Fresh000
Picked011
Done000
Total47855
Error
0.2b
Counts
55 → 8
Alt Table
StatusErrorProgram
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re))))
41.8b
(*.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
47.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
29.3b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
48.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
53.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
49.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (-.f64 (*.f64 (/.f64 (*.f64 im im) re) -1/2) re) re))))
38.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
Compiler

Compiled 1096 to 720 computations (34.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite117.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
41×add-sqr-sqrt_binary64
33×sqrt-prod_binary64
26×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
22×times-frac_binary64
Counts
4 → 110
Calls

4 calls:

8.0ms
(*.f64 re (sqrt.f64 (/.f64 1 im)))
7.0ms
(*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)
7.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))
3.0ms
(sqrt.f64 (/.f64 1 im))
Compiler

Compiled 2353 to 1775 computations (24.6% saved)

series67.0ms (1.3%)

Error
0.2b
Counts
4 → 24
Calls

4 calls:

27.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))
16.0ms
(*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)
15.0ms
(*.f64 re (sqrt.f64 (/.f64 1 im)))
6.0ms
(sqrt.f64 (/.f64 1 im))
Compiler

Compiled 952 to 789 computations (17.1% saved)

simplify110.0ms (2.1%)

Algorithm
egg-herbie
Rules
407×associate-*l/_binary64
391×distribute-rgt-neg-in_binary64
376×times-frac_binary64
357×distribute-lft-neg-in_binary64
311×*-commutative_binary64
Counts
134 → 77
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01542027
13261896
210451896
322361896
449381896
549871896

prune52.0ms (1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New73477
Fresh066
Picked011
Done011
Total731285
Error
0.2b
Counts
85 → 12
Alt Table
StatusErrorProgram
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re))))
29.7b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))))) (sqrt.f64 (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))))
47.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
41.5b
(*.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im)))))) 3)))
29.4b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))))
29.7b
(*.f64 1/2 (/.f64 (*.f64 (sqrt.f64 2) (-.f64 im (*.f64 re (*.f64 1/4 (/.f64 re im))))) (+.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
41.8b
(*.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
29.3b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
48.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
53.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
49.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (-.f64 (*.f64 (/.f64 (*.f64 im im) re) -1/2) re) re))))
38.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
Compiler

Compiled 1551 to 1170 computations (24.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite122.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
37×sqrt-prod_binary64
36×add-sqr-sqrt_binary64
27×associate-*r*_binary64
22×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
Counts
4 → 108
Calls

4 calls:

12.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2))))
9.0ms
(*.f64 (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))
8.0ms
(*.f64 re (sqrt.f64 (/.f64 1 im)))
7.0ms
(*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))
Compiler

Compiled 2835 to 2268 computations (20% saved)

series98.0ms (1.9%)

Error
0.2b
Counts
4 → 30
Calls

4 calls:

30.0ms
(*.f64 (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))
29.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2))))
17.0ms
(*.f64 re (sqrt.f64 (/.f64 1 im)))
17.0ms
(*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))
Compiler

Compiled 1323 to 1140 computations (13.8% saved)

simplify152.0ms (2.9%)

Algorithm
egg-herbie
Rules
414×*-commutative_binary64
393×times-frac_binary64
379×distribute-rgt-neg-in_binary64
349×distribute-lft-neg-in_binary64
224×associate-*r*_binary64
Counts
138 → 104
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01742911
13752546
211842505
326032505
447672505
549992505
649512505

prune65.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1022104
Fresh279
Picked101
Done112
Total10610116
Error
0.2b
Counts
116 → 10
Alt Table
StatusErrorProgram
47.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
41.5b
(*.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im)))))) 3)))
29.3b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (*.f64 (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))))
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re))))
41.8b
(*.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
29.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sqrt.f64 (*.f64 im (sqrt.f64 2))) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im)))))))
48.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
53.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
49.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (-.f64 (*.f64 (/.f64 (*.f64 im im) re) -1/2) re) re))))
38.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
Compiler

Compiled 2085 to 1656 computations (20.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im))))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sqrt.f64 (*.f64 im (sqrt.f64 2))) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im))))))
0.4b
(/.f64 (sqrt.f64 2) im)
0.5b
(*.f64 im (sqrt.f64 2))

rewrite119.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
37×add-sqr-sqrt_binary64
28×sqrt-prod_binary64
27×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
18×times-frac_binary64
Counts
4 → 112
Calls

4 calls:

9.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sqrt.f64 (*.f64 im (sqrt.f64 2))) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im))))))
8.0ms
(*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im))))
4.0ms
(*.f64 im (sqrt.f64 2))
4.0ms
(/.f64 (sqrt.f64 2) im)
Compiler

Compiled 2828 to 2399 computations (15.2% saved)

series77.0ms (1.5%)

Error
0.2b
Counts
4 → 21
Calls

4 calls:

38.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sqrt.f64 (*.f64 im (sqrt.f64 2))) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im))))))
22.0ms
(*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im))))
7.0ms
(*.f64 im (sqrt.f64 2))
7.0ms
(/.f64 (sqrt.f64 2) im)
Compiler

Compiled 1024 to 889 computations (13.2% saved)

simplify155.0ms (2.9%)

Algorithm
egg-herbie
Rules
477×associate-/l*_binary64
432×*-commutative_binary64
342×times-frac_binary64
245×cancel-sign-sub-inv_binary64
213×associate-*l/_binary64
Counts
133 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01902592
14012446
214232424
338752424
447582424
549612424
649042424

prune50.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New78078
Fresh088
Picked011
Done011
Total781088
Error
0.2b
Counts
88 → 10
Alt Table
StatusErrorProgram
47.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
41.5b
(*.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im)))))) 3)))
29.3b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (*.f64 (-.f64 (sqrt.f64 im) (*.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))))
32.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (+.f64 im (*.f64 1/2 (/.f64 (*.f64 re re) im))) re))))
41.8b
(*.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))))))
29.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sqrt.f64 (*.f64 im (sqrt.f64 2))) (*.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 (sqrt.f64 2) im)))))))
48.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 re -2))))
53.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
49.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (-.f64 (*.f64 (/.f64 (*.f64 im im) re) -1/2) re) re))))
38.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
Compiler

Compiled 1568 to 1327 computations (15.4% saved)

regimes1.6s (30.1%)

Accuracy

Total 13.7b remaining (96.9%)

Threshold costs 0b (0%)

Compiler

Compiled 16284 to 11922 computations (26.8% saved)

bsearch56.0ms (1%)

Steps
ItersRangePoint
5
1.1241956541430794e-71
2.7767684379002207e-71
1.6542415558306005e-71
7
-6.251626431572681e-161
-4.6886663057515814e-163
-4.7654028522434134e-163
9
-5.971664172296382e+155
-7.184710672342132e+148
-2.011934090315106e+152
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
04599
16599
27099
37299
47399
57299

end1.0ms (0%)

Compiler

Compiled 67 to 50 computations (25.4% saved)

sample1.6s (29.7%)

Algorithm
intervals
Results
400.0ms6082×body128valid
200.0ms657×body2048valid
188.0ms505×body4096valid
133.0ms8000×pre128true
106.0ms418×body1024valid
35.0ms201×body512valid
25.0ms137×body256valid
Compiler

Compiled 279 to 218 computations (21.9% saved)

Profiling

Loading profile data...