Details

Time bar (total: 3.4s)

analyze468.0ms (13.6%)

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)

sample1.9s (54.6%)

Results
801.0ms6213×body128valid
357.0ms661×body2048valid
351.0ms568×body4096valid
179.0ms452×body1024valid
104.0ms238×body512valid
28.0ms124×body256valid
Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify35.0ms (1%)

Algorithm
1×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

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
15.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
38.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
Compiler

Compiled 85 to 61 computations (28.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(hypot.f64 re im)
✓0.5b
(-.f64 (hypot.f64 re im) re)

series25.0ms (0.7%)

Counts
2 → 48
Calls

2 calls:

14.0ms
(-.f64 (hypot.f64 re im) re)
11.0ms
(hypot.f64 re im)

rewrite6.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
9×prod-diff_binary64
4×add-log-exp_binary64
Counts
2 → 40
Calls

2 calls:

4.0ms
(-.f64 (hypot.f64 re im) re)
0.0ms
(hypot.f64 re im)

simplify76.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
952×fma-neg_binary64
648×fma-def_binary64
605×times-frac_binary64
452×associate-*l*_binary64
282×associate-/r*_binary64
Counts
88 → 104
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01431564
13611325
211771271
346761269
452701269

prune60.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1022104
Fresh101
Picked011
Done000
Total1033106
Error
9.2b
Counts
106 → 3
Alt Table
StatusErrorProgram
✓15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
54.7b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶31.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 im)))
Compiler

Compiled 2200 to 1338 computations (39.2% saved)

localize4.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done011
Total033
Error
9.2b
Counts
3 → 3
Alt Table
StatusErrorProgram
✓15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
▶54.7b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓31.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 im)))
Compiler

Compiled 48 to 40 computations (16.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓0.0b
(*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))
✓8.8b
(/.f64 (pow.f64 im 2) re)
✓18.3b
(sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re))))

series58.0ms (1.7%)

Counts
4 → 48
Calls

4 calls:

21.0ms
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
15.0ms
(sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re))))
11.0ms
(/.f64 (pow.f64 im 2) re)
10.0ms
(*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))

rewrite30.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
27×add-exp-log_binary64
26×add-sqr-sqrt_binary64
24×times-frac_binary64
24×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
Counts
4 → 113
Calls

4 calls:

8.0ms
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
7.0ms
(*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))
6.0ms
(sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re))))
3.0ms
(/.f64 (pow.f64 im 2) re)

simplify99.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
680×fma-neg_binary64
373×unswap-sqr_binary64
323×associate-/l*_binary64
310×associate-*r/_binary64
307×associate-*l/_binary64
Counts
161 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01762087
13041706
27841693
329181693
444851693
550951693

prune101.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1662168
Fresh000
Picked011
Done112
Total1674171
Error
0.0b
Counts
171 → 4
Alt Table
StatusErrorProgram
✓15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
✓54.7b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
45.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 re)) im))
▶45.2b
(/.f64 (*.f64 im 1/2) (sqrt.f64 re))
Compiler

Compiled 3065 to 2184 computations (28.7% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series30.0ms (0.9%)

Counts
1 → 12
Calls

1 calls:

30.0ms
(/.f64 (*.f64 im 1/2) (sqrt.f64 re))

rewrite5.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
6×associate-/r*_binary64
6×sqrt-prod_binary64
6×times-frac_binary64
6×add-cbrt-cube_binary64
6×add-exp-log_binary64
Counts
1 → 29
Calls

1 calls:

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

simplify125.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
1017×div-sub_binary64
819×associate-/r/_binary64
513×associate-*r*_binary64
489×distribute-rgt-in_binary64
299×sub-neg_binary64
Counts
41 → 43
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
066534
1138477
2420477
31525476
42307476
52418476
63061476
74057476
83982476
94372476
104987476
114559476

prune21.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New41243
Fresh011
Picked011
Done022
Total41647
Error
0b
Counts
47 → 6
Alt Table
StatusErrorProgram
45.3b
(*.f64 (sqrt.f64 (/.f64 (*.f64 im 1/2) (sqrt.f64 re))) (sqrt.f64 (/.f64 (*.f64 im 1/2) (sqrt.f64 re))))
45.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 re)) im))
✓15.2b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
✓54.7b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
45.7b
(/.f64 1 (/.f64 (sqrt.f64 re) (*.f64 im 1/2)))
✓45.2b
(/.f64 (*.f64 im 1/2) (sqrt.f64 re))
Compiler

Compiled 546 to 309 computations (43.4% saved)

regimes279.0ms (8.1%)

Accuracy

Total 8.4b remaining (98.3%)

Threshold costs 0b (0%)

Counts
32 → 2
Compiler

Compiled 3113 to 2351 computations (24.5% saved)

bsearch30.0ms (0.9%)

Steps
ItersRangePoint
8
1.37580405100101e-118
1.6681614645466336e-114
1.6248919274963702e-114
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01730
12230
22730
32930
43030
53030

end77.0ms (2.2%)

Compiler

Compiled 115 to 87 computations (24.3% saved)

Profiling

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