Details

Time bar (total: 5.0s)

analyze609.0ms (12.3%)

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 (39.2%)

Results
880.0ms6280×body128valid
392.0ms519×body4096valid
338.0ms663×body2048valid
178.0ms422×body1024valid
74.0ms239×body512valid
30.0ms133×body256valid
Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify32.0ms (0.7%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
11.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
35.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))
▶11.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 85 to 61 computations (28.2% 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)
✓0.9b
(-.f64 (hypot.f64 re im) re)

series79.0ms (1.6%)

Counts
3 → 56
Calls

3 calls:

44.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
23.0ms
(hypot.f64 re im)
12.0ms
(-.f64 (hypot.f64 re im) re)

rewrite241.0ms (4.9%)

Algorithm
3×egg-rewrite
Rules
88×egg
39×egg
25×egg
Counts
3 → 152
Calls

3 calls:

112.0ms
(-.f64 (hypot.f64 re im) re)
74.0ms
(hypot.f64 re im)
51.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11117
214277
348567
448267
549797
044
1794
28694
347304
456654
0812
117212
2205312
3573512

simplify85.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
618×fma-def_binary64
559×fma-neg_binary64
365×associate-/l*_binary64
347×times-frac_binary64
280×cancel-sign-sub-inv_binary64
Counts
208 → 224
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01581505
14891464
215851399
347931395
450571395

prune131.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2204224
Fresh101
Picked011
Done000
Total2215226
Error
0.1b
Counts
226 → 5
Alt Table
StatusErrorProgram
55.6b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (*.f64 1/32 (/.f64 (*.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2))) (*.f64 1/256 (/.f64 (*.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
✓11.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
▶12.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
56.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
49.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
Compiler

Compiled 4821 to 3077 computations (36.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))
0.0b
(hypot.f64 re im)
✓0.5b
(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)
✓7.4b
(-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)

series85.0ms (1.7%)

Counts
3 → 40
Calls

3 calls:

43.0ms
(sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))
28.0ms
(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)
13.0ms
(-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)

rewrite180.0ms (3.6%)

Algorithm
3×egg-rewrite
Rules
74×egg
46×egg
27×egg
Counts
3 → 147
Calls

3 calls:

75.0ms
(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)
53.0ms
(sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))
50.0ms
(-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
087
11577
217947
351567
074
11254
212414
348484
449784
01012
119612
2222412
3615612

simplify77.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
595×fma-def_binary64
425×fma-neg_binary64
365×associate-/l*_binary64
347×times-frac_binary64
260×cancel-sign-sub-inv_binary64
Counts
187 → 202
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01511177
14601148
214971091
349021087
450861087

prune149.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2680268
Fresh033
Picked011
Done011
Total2685273
Error
0.1b
Counts
273 → 5
Alt Table
StatusErrorProgram
55.6b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (*.f64 1/32 (/.f64 (*.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2))) (*.f64 1/256 (/.f64 (*.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
✓11.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
✓12.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
56.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶49.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
Compiler

Compiled 5993 to 3837 computations (36% saved)

localize10.0ms (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 2) im)
✓0.5b
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im))

series37.0ms (0.7%)

Counts
4 → 0
Calls

4 calls:

23.0ms
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
5.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im))
5.0ms
(sqrt.f64 (/.f64 1 re))
3.0ms
(*.f64 (sqrt.f64 2) im)

rewrite270.0ms (5.4%)

Algorithm
4×egg-rewrite
Rules
64×egg
59×egg
57×egg
38×egg
Counts
4 → 216
Calls

4 calls:

84.0ms
(sqrt.f64 (/.f64 1 re))
83.0ms
(*.f64 (sqrt.f64 2) im)
55.0ms
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
44.0ms
(*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
081
11591
214071
350121
056
1996
210296
348236
459486
01319
12586
224586
355066
056
1984
210144
347694
450974

simplify9.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
216 → 214
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune117.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2095214
Fresh202
Picked101
Done022
Total2127219
Error
0.0b
Counts
219 → 7
Alt Table
StatusErrorProgram
✓12.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
49.5b
(*.f64 1/2 (pow.f64 (sqrt.f64 (/.f64 im (sqrt.f64 re))) 2))
52.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (*.f64 (pow.f64 (pow.f64 (/.f64 1 re) 4/3) 1/3) (cbrt.f64 (pow.f64 re -1/6)))))
49.5b
(*.f64 1/2 (*.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (pow.f64 re -1/2))))
▶49.5b
(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
✓11.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
49.6b
(*.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 im) 2) (sqrt.f64 (/.f64 1 re))))
Compiler

Compiled 3717 to 3013 computations (18.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series22.0ms (0.4%)

Counts
1 → 12
Calls

1 calls:

22.0ms
(/.f64 im (sqrt.f64 re))

rewrite45.0ms (0.9%)

Algorithm
1×egg-rewrite
Rules
76×egg
Counts
1 → 76
Calls

1 calls:

44.0ms
(/.f64 im (sqrt.f64 re))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11036
212936
350176

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
1×1-exp_binary64
Counts
88 → 77
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07108
110108
29108

prune35.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New76177
Fresh134
Picked101
Done022
Total78684
Error
0.0b
Counts
84 → 6
Alt Table
StatusErrorProgram
✓12.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
49.5b
(*.f64 1/2 (pow.f64 (sqrt.f64 (/.f64 im (sqrt.f64 re))) 2))
52.6b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (*.f64 (pow.f64 (pow.f64 (/.f64 1 re) 4/3) 1/3) (cbrt.f64 (pow.f64 re -1/6)))))
49.5b
(*.f64 1/2 (*.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (pow.f64 re -1/2))))
49.7b
(*.f64 1/2 (/.f64 1 (/.f64 (sqrt.f64 re) im)))
✓11.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 1073 to 587 computations (45.3% saved)

regimes677.0ms (13.6%)

Accuracy

Total 6.2b remaining (97.1%)

Threshold costs 0b (0%)

Counts
52 → 2
Compiler

Compiled 5508 to 4469 computations (18.9% saved)

bsearch1.0ms (0%)

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02345
13145
23645
33845
43945
53945

end92.0ms (1.9%)

Compiler

Compiled 149 to 112 computations (24.8% saved)

Profiling

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