Details

Time bar (total: 4.6s)

analyze482.0ms (10.5%)

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)

sample1.8s (39.3%)

Results
827.0ms6317×body128valid
354.0ms503×body4096valid
342.0ms660×body2048valid
167.0ms408×body1024valid
78.0ms245×body512valid
27.0ms123×body256valid
Compiler

Compiled 40 to 28 computations (30% saved)

preprocess33.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
316×fma-def_binary64
164×fma-neg_binary64
86×distribute-rgt-in_binary64
48×distribute-lft-in_binary64
48×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01930
13330
25130
38830
413530
518530
630530
747830
868230
983330
10108330
11124330
12126130
13126530
022
Stop Event
1×saturated
1×saturated
Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify23.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
201×fma-def_binary64
142×fma-neg_binary64
51×distribute-rgt-in_binary64
43×cancel-sign-sub-inv_binary64
27×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01315
12015
23315
35315
48015
510915
618015
728615
841015
949315
1061015
1168215
1270515
1374415
1479315
1585615
1689215
1790115
Stop Event
1×saturated
Counts
1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
12.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶12.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series45.0ms (1%)

Counts
2 → 32
Calls

12 calls:

10.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
im
0
7.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
im
-inf
6.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
im
inf
5.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
re
inf
4.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
re
-inf

rewrite46.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
811×log1p-expm1-u_binary64
811×expm1-log1p-u_binary64
410×prod-diff_binary64
86×add-sqr-sqrt_binary64
82×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0819
117319
2218619
Stop Event
1×node limit
Counts
2 → 74

simplify35.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
527×fma-def_binary64
371×associate-*l*_binary64
337×associate-/l*_binary64
311×times-frac_binary64
236×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01401017
1421994
21460945
Stop Event
1×node limit
Counts
106 → 119

prune117.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1136119
Fresh000
Picked011
Done000
Total1137120
Error
0.1b
Counts
120 → 7
Alt Table
StatusErrorProgram
52.1b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (*.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16))))
47.9b
(*.f64 1/2 (*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))))
47.9b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
▶31.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))))
56.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 1/2 (*.f64 (/.f64 im re) im) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))
56.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 1/2 re) (*.f64 im im)))))
✓12.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 2797 to 1912 computations (31.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))
✓0.2b
(sqrt.f64 (/.f64 1 im))
✓0.3b
(*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))
✓0.4b
(*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))

series63.0ms (1.4%)

Counts
4 → 36
Calls

21 calls:

7.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))
im
-inf
5.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))
im
0
4.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))
im
inf
4.0ms
(-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))
re
0
4.0ms
(*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))
re
0

rewrite89.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
915×prod-diff_binary64
234×egg-rr
136×add-sqr-sqrt_binary64
131×log1p-expm1-u_binary64
131×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01457
129446
2356046
Stop Event
1×node limit
Counts
4 → 234

simplify59.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
401×fma-def_binary64
385×fma-neg_binary64
154×cancel-sign-sub-inv_binary64
138×associate-*l*_binary64
127×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
021609
148591
2115528
3319528
4558528
5761528
61051528
71320528
81822528
92015528
102123528
112123528
Stop Event
1×saturated
Counts
270 → 246

prune186.0ms (4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2460246
Fresh055
Picked011
Done011
Total2467253
Error
0.1b
Counts
253 → 7
Alt Table
StatusErrorProgram
52.1b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (*.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16))))
▶47.9b
(*.f64 1/2 (*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))))
47.9b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓31.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))))
56.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 1/2 (*.f64 (/.f64 im re) im) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))
56.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 1/2 re) (*.f64 im im)))))
✓12.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 8388 to 5555 computations (33.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (/.f64 1 re))
✓0.2b
(*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
✓0.2b
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))
✓0.4b
(*.f64 im (sqrt.f64 2))

series37.0ms (0.8%)

Counts
4 → 24
Calls

15 calls:

5.0ms
(*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
im
inf
5.0ms
(*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
im
-inf
4.0ms
(*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
im
0
4.0ms
(*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
re
-inf
3.0ms
(*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
re
inf

rewrite47.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
574×log-prod_binary64
203×expm1-udef_binary64
203×log1p-udef_binary64
191×log-pow_binary64
189×pow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01338
126328
2291828
Stop Event
1×node limit
Counts
4 → 91

simplify15.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
26×associate-*l*_binary64
16×associate-*r*_binary64
14×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
013300
122300
243300
382300
486300
Stop Event
1×saturated
Counts
115 → 94

prune63.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New87794
Fresh404
Picked101
Done022
Total929101
Error
0b
Counts
101 → 9
Alt Table
StatusErrorProgram
51.3b
(*.f64 1/2 (*.f64 (*.f64 im (sqrt.f64 2)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1/2 re)) 3))))
47.9b
(*.f64 1/2 (*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 (pow.f64 re -1/2)) 2))))
47.9b
(*.f64 1/2 (*.f64 (*.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 re -1/2))))
✓31.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))))
47.8b
(*.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))) 2))
48.0b
(*.f64 1/2 (pow.f64 (cbrt.f64 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))) 3))
▶47.8b
(*.f64 1/2 (+.f64 0 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
✓12.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
47.9b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 im (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 re)))))
Compiler

Compiled 1777 to 1511 computations (15% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/2 (+.f64 0 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
✓0.0b
(*.f64 2 (/.f64 1/2 re))
✓0.1b
(sqrt.f64 (*.f64 2 (/.f64 1/2 re)))
✓0.1b
(*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))

series36.0ms (0.8%)

Counts
4 → 36
Calls

18 calls:

3.0ms
(*.f64 2 (/.f64 1/2 re))
re
-inf
3.0ms
(*.f64 1/2 (+.f64 0 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
re
-inf
3.0ms
(*.f64 1/2 (+.f64 0 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
im
inf
3.0ms
(*.f64 1/2 (+.f64 0 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
im
-inf
2.0ms
(*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))
im
-inf

rewrite54.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
494×log-prod_binary64
182×expm1-udef_binary64
182×log1p-udef_binary64
165×pow3_binary64
160×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01231
126331
2287231
Stop Event
1×node limit
Counts
4 → 141

simplify14.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
5×*-commutative_binary64
3×associate-*r*_binary64
3×associate-*l*_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09300
115300
222300
324300
Stop Event
1×saturated
Counts
177 → 144

prune100.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1413144
Fresh516
Picked101
Done022
Total1476153
Error
0b
Counts
153 → 6
Alt Table
StatusErrorProgram
47.8b
(*.f64 1/2 (+.f64 0 (fma.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1/2 re)) 0)))
47.8b
(*.f64 1/2 (+.f64 0 (fma.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (/.f64 1 (sqrt.f64 re))) 0)))
✓31.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))))
47.8b
(*.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im 1/2))
48.0b
(*.f64 1/2 (pow.f64 (cbrt.f64 (*.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))) 3))
✓12.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 2238 to 1644 computations (26.5% saved)

regimes1.1s (24.3%)

Accuracy

Total 5.7b remaining (98.2%)

Threshold costs 0b (0%)

Counts
100 → 2
Compiler

Compiled 10652 to 8954 computations (15.9% saved)

bsearch3.0ms (0.1%)

Algorithm
1×left-value
Calls

1 calls:

0.0ms
(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)
Steps
ItersPointRange
0.0
∈ [
0.0
, 
6.017813989273321e-281
]
Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (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
02447
13347
23847
34047
44147
Stop Event
1×saturated

end91.0ms (2%)

Stop Event
1×fuel
Compiler

Compiled 154 to 118 computations (23.4% saved)

Profiling

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