Details

Time bar (total: 12.4s)

analyze1.3s (10.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
3.1%96.8%0.1%6
15.6%81.2%3.2%7
23.4%72.6%4%8
32.4%56.2%11.4%9
36.3%51.7%12%10
40.7%42.9%16.4%11
42.6%40.3%17.1%12
44.5%35.7%19.8%13
45.5%34.4%20.1%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample191.0ms (1.5%)

Algorithm
intervals
Results
89.0ms60×body2048valid
56.0ms87×body1024valid
9.0ms28×body512valid
6.0ms64×body128valid
5.0msbody1024invalid
3.0ms17×body256valid
3.0msbody512invalid
3.0msbody2048invalid
2.0ms16×body128invalid
1.0ms14×body128nan
1.0msbody256invalid
Compiler

Compiled 37 to 25 computations (32.4% saved)

simplify51.0ms (0.4%)

Algorithm
egg-herbie
Rules
701×fma-def_binary64
563×associate-/r/_binary64
484×associate-/r*_binary64
474×associate-*l/_binary64
421×associate-/l/_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01122
12922
26720
316420
446320
5176120
6484720
7501320

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
48.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
49.0b
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
49.0b
(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
Compiler

Compiled 97 to 63 computations (35.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
2.2b
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.3b
(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.9b
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series372.0ms (3%)

Counts
4 → 96
Calls

4 calls:

149.0ms
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
113.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
59.0ms
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
32.0ms
(pow.f64 (+.f64 1 (/.f64 i n)) n)

rewrite213.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
584×times-frac_binary64
502×add-sqr-sqrt_binary64
391×*-un-lft-identity_binary64
241×add-cube-cbrt_binary64
174×associate-*r*_binary64
Counts
4 → 494
Calls

4 calls:

56.0ms
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
26.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms
(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify560.0ms (4.5%)

Algorithm
egg-herbie
Rules
961×fma-def_binary64
386×times-frac_binary64
336×*-commutative_binary64
275×+-commutative_binary64
222×associate-*r/_binary64
Counts
590 → 793
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0112323638
1350323269
2497423269

prune928.0ms (7.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New7867793
Fresh011
Picked101
Done000
Total7878795
Error
0.1b
Counts
795 → 8
Alt Table
StatusErrorProgram
49.0b
(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
22.2b
(*.f64 100 (/.f64 (*.f64 n (expm1.f64 i)) i))
26.6b
(-.f64 (fma.f64 (*.f64 n (*.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (*.f64 n i) 50 (*.f64 (/.f64 (*.f64 i i) n) 100/3)))) (*.f64 50 (+.f64 i (*.f64 i i))))
47.9b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
56.4b
(*.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (*.f64 n n))))
55.7b
(*.f64 100 (/.f64 (*.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
54.5b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))
49.0b
(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
Compiler

Compiled 31500 to 17896 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 100 (/.f64 (*.f64 n (expm1.f64 i)) i))
7.7b
(/.f64 (*.f64 n (expm1.f64 i)) i)

series40.0ms (0.3%)

Counts
2 → 48
Calls

2 calls:

20.0ms
(*.f64 100 (/.f64 (*.f64 n (expm1.f64 i)) i))
20.0ms
(/.f64 (*.f64 n (expm1.f64 i)) i)

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
add-sqr-sqrt_binary64
associate-*r*_binary64
*-un-lft-identity_binary64
Counts
2 → 52
Calls

2 calls:

13.0ms
(*.f64 100 (/.f64 (*.f64 n (expm1.f64 i)) i))
5.0ms
(/.f64 (*.f64 n (expm1.f64 i)) i)

simplify96.0ms (0.8%)

Algorithm
egg-herbie
Rules
857×fma-def_binary64
716×times-frac_binary64
601×associate-/l*_binary64
233×associate-/r*_binary64
214×distribute-rgt-in_binary64
Counts
100 → 94
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321390
13211231
210881220
348461205
454231205

prune93.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New92294
Fresh077
Picked101
Done000
Total939102
Error
0.1b
Counts
102 → 9
Alt Table
StatusErrorProgram
17.8b
(*.f64 100 (*.f64 n (/.f64 (expm1.f64 i) i)))
54.5b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))
26.6b
(-.f64 (fma.f64 (*.f64 n (*.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (*.f64 n i) 50 (*.f64 (/.f64 (*.f64 i i) n) 100/3)))) (*.f64 50 (+.f64 i (*.f64 i i))))
49.0b
(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
47.9b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
56.4b
(*.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (*.f64 n n))))
55.7b
(*.f64 100 (/.f64 (*.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
49.0b
(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
17.8b
(*.f64 (*.f64 n 100) (/.f64 (expm1.f64 i) i))
Compiler

Compiled 1553 to 722 computations (53.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (*.f64 n 100) (/.f64 (expm1.f64 i) i))

series23.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

23.0ms
(*.f64 (*.f64 n 100) (/.f64 (expm1.f64 i) i))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×associate-*r*_binary64
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
times-frac_binary64
*-un-lft-identity_binary64
Counts
1 → 35
Calls

1 calls:

8.0ms
(*.f64 (*.f64 n 100) (/.f64 (expm1.f64 i) i))

simplify100.0ms (0.8%)

Algorithm
egg-herbie
Rules
538×fma-def_binary64
382×associate-*r/_binary64
375×associate-/l*_binary64
341×times-frac_binary64
322×associate-*l/_binary64
Counts
59 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0111913
1303803
21151800
33755791
44752791
54956791

prune61.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New65065
Fresh088
Picked011
Done000
Total65974
Error
0.1b
Counts
74 → 9
Alt Table
StatusErrorProgram
17.8b
(*.f64 100 (*.f64 n (/.f64 (expm1.f64 i) i)))
54.5b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))
26.6b
(-.f64 (fma.f64 (*.f64 n (*.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (*.f64 n i) 50 (*.f64 (/.f64 (*.f64 i i) n) 100/3)))) (*.f64 50 (+.f64 i (*.f64 i i))))
49.0b
(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
47.9b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
56.4b
(*.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (*.f64 n n))))
55.7b
(*.f64 100 (/.f64 (*.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
49.0b
(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
17.8b
(*.f64 (*.f64 n 100) (/.f64 (expm1.f64 i) i))
Compiler

Compiled 1269 to 607 computations (52.2% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 n (/.f64 (expm1.f64 i) i))
0.0b
(*.f64 100 (*.f64 n (/.f64 (expm1.f64 i) i)))

series39.0ms (0.3%)

Counts
2 → 48
Calls

2 calls:

20.0ms
(*.f64 n (/.f64 (expm1.f64 i) i))
19.0ms
(*.f64 100 (*.f64 n (/.f64 (expm1.f64 i) i)))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
14×associate-*r*_binary64
11×*-un-lft-identity_binary64
Counts
2 → 57
Calls

2 calls:

8.0ms
(*.f64 100 (*.f64 n (/.f64 (expm1.f64 i) i)))
7.0ms
(*.f64 n (/.f64 (expm1.f64 i) i))

simplify123.0ms (1%)

Algorithm
egg-herbie
Rules
769×fma-def_binary64
479×associate-*r/_binary64
431×associate-*l/_binary64
292×associate-/l*_binary64
240×times-frac_binary64
Counts
105 → 105
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01441455
13541296
212451285
344721270
449991270
549501270

prune82.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1050105
Fresh077
Picked011
Done011
Total1059114
Error
0.1b
Counts
114 → 9
Alt Table
StatusErrorProgram
17.8b
(*.f64 100 (*.f64 n (/.f64 (expm1.f64 i) i)))
54.5b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))
26.6b
(-.f64 (fma.f64 (*.f64 n (*.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (*.f64 n i) 50 (*.f64 (/.f64 (*.f64 i i) n) 100/3)))) (*.f64 50 (+.f64 i (*.f64 i i))))
49.0b
(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
47.9b
(*.f64 100 (/.f64 (expm1.f64 (*.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
56.4b
(*.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (*.f64 n n))))
55.7b
(*.f64 100 (/.f64 (*.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
49.0b
(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
17.8b
(*.f64 (*.f64 n 100) (/.f64 (expm1.f64 i) i))
Compiler

Compiled 1605 to 698 computations (56.5% saved)

regimes1.4s (11.2%)

Accuracy

Total 11.8b remaining (98.8%)

Threshold costs 0b (0%)

Counts
123 → 4
Compiler

Compiled 8968 to 6052 computations (32.5% saved)

bsearch287.0ms (2.3%)

Steps
ItersRangePoint
5
5.472855123833153e+233
1.4958304873507775e+234
8.043070052233076e+233
10
2.4660162603740665e+101
7.4792596205815625e+112
5.111910710628546e+112
10
1.0642461942078875e-7
1366.181905434224
346.1220968706167
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03782
15082
25482
35682
45782
55482

end1.0ms (0%)

Compiler

Compiled 57 to 38 computations (33.3% saved)

sample6.3s (51%)

Algorithm
intervals
Results
2.6s1731×body2048valid
1.9s2570×body1024valid
407.0ms1225×body512valid
181.0ms1872×body128valid
137.0ms180×body1024invalid
115.0ms227×body512invalid
105.0ms567×body256valid
96.0ms35×body4096valid
59.0ms469×body128invalid
46.0ms164×body256invalid
42.0ms21×body2048invalid
19.0ms316×body128nan
Compiler

Compiled 228 to 152 computations (33.3% saved)

Profiling

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