Details

Time bar (total: 16.5s)

analyze968.0ms (5.9%)

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
25%62.4%12.6%5
25%56.2%18.8%6
28.1%46.8%25.1%7
28.1%43.7%28.2%8
29.7%34.3%36%9
29.7%31.6%38.7%10
31.1%25.8%43.1%11
31.1%24.6%44.3%12
31.5%21.9%46.6%13
31.5%21%47.5%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample8.5s (51.8%)

Results
2.2s2695×body1024valid
2.0s1769×body1024invalid
1.6s1789×body2048valid
892.0ms1304×body512valid
747.0ms955×body512invalid
338.0ms1857×body128valid
271.0ms611×body256valid
218.0ms533×body256invalid
193.0ms1061×body128invalid
20.0ms12×body2048invalid
Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify60.0ms (0.4%)

Algorithm
egg-herbie
Rules
436×unswap-sqr_binary64
377×fma-def_binary64
359×sub-neg_binary64
289×unsub-neg_binary64
253×distribute-rgt-neg-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
12019
24119
310219
424819
579019
6211019
7440519
8504819

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
31.6b
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
Compiler

Compiled 45 to 33 computations (26.7% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
2.3b
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series33.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

33.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite20.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
69×unpow-prod-down_binary64
58×*-un-lft-identity_binary64
56×prod-diff_binary64
47×add-sqr-sqrt_binary64
35×add-cube-cbrt_binary64
Counts
1 → 96
Calls

1 calls:

10.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify166.0ms (1%)

Algorithm
egg-herbie
Rules
677×fma-neg_binary64
428×cancel-sign-sub-inv_binary64
331×sub-neg_binary64
201×sqr-pow_binary64
199×neg-mul-1_binary64
Counts
120 → 142
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03337264
18165604
228523731
339553731
448343731
547513731

prune202.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1375142
Fresh000
Picked101
Done000
Total1385143
Error
0.8b
Counts
143 → 5
Alt Table
StatusErrorProgram
33.0b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1 (/.f64 (log.f64 (/.f64 1 x)) n))) (*.f64 (pow.f64 n 2) (pow.f64 x 2)))) (/.f64 (exp.f64 (*.f64 -1 (/.f64 (log.f64 (/.f64 1 x)) n))) (*.f64 n x))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1 (/.f64 (log.f64 (/.f64 1 x)) n))) (*.f64 n (pow.f64 x 2)))))
24.7b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
19.6b
(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
31.1b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
36.1b
(-.f64 (+.f64 (+.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n)) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (*.f64 x x) (*.f64 n n))) (fma.f64 1/24 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (pow.f64 x 4) (pow.f64 n 4))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 3)) (+.f64 (/.f64 1/3 n) (/.f64 1/6 (pow.f64 n 3))))))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 4)) (-.f64 (/.f64 11/24 (*.f64 n n)) (/.f64 1/4 (pow.f64 n 3))))) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 n (*.f64 n (pow.f64 x 3)))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) n) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4))))))
Compiler

Compiled 6580 to 4510 computations (31.5% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
3.9b
(-.f64 (log1p.f64 x) (log.f64 x))

series474.0ms (2.9%)

Counts
2 → 36
Calls

2 calls:

471.0ms
(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
3.0ms
(-.f64 (log1p.f64 x) (log.f64 x))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity_binary64
33×add-sqr-sqrt_binary64
23×add-cube-cbrt_binary64
18×times-frac_binary64
12×prod-diff_binary64
Counts
2 → 83
Calls

2 calls:

5.0ms
(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
4.0ms
(-.f64 (log1p.f64 x) (log.f64 x))

simplify123.0ms (0.7%)

Algorithm
egg-herbie
Rules
869×fma-neg_binary64
399×fma-def_binary64
386×associate-*l*_binary64
296×associate-*r*_binary64
171×associate-/l*_binary64
Counts
119 → 118
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01892225
14261862
212171802
340711801
449621801
549711801
649341801

prune118.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1108118
Fresh134
Picked101
Done000
Total11211123
Error
0.1b
Counts
123 → 11
Alt Table
StatusErrorProgram
38.5b
(/.f64 (+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))) n)
20.1b
(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (*.f64 n (+.f64 (*.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (*.f64 (log.f64 x) (log.f64 x)) (*.f64 (log1p.f64 x) (log.f64 x))))))
19.7b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (-.f64 (log1p.f64 x) (log.f64 x))) (-.f64 (log1p.f64 x) (log.f64 x)))) n)
19.5b
(/.f64 (log.f64 (/.f64 (+.f64 1 x) x)) n)
19.6b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
24.7b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
19.6b
(*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) n))
19.6b
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
35.0b
(/.f64 (-.f64 (-.f64 (log1p.f64 x) (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (log.f64 (cbrt.f64 x))) n)
31.1b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
36.1b
(-.f64 (+.f64 (+.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n)) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (*.f64 x x) (*.f64 n n))) (fma.f64 1/24 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (pow.f64 x 4) (pow.f64 n 4))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 3)) (+.f64 (/.f64 1/3 n) (/.f64 1/6 (pow.f64 n 3))))))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 4)) (-.f64 (/.f64 11/24 (*.f64 n n)) (/.f64 1/4 (pow.f64 n 3))))) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 n (*.f64 n (pow.f64 x 3)))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) n) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4))))))
Compiler

Compiled 2556 to 952 computations (62.8% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 1 x) x)
0.1b
(/.f64 (log.f64 (/.f64 (+.f64 1 x) x)) n)
4.4b
(log.f64 (/.f64 (+.f64 1 x) x))

series375.0ms (2.3%)

Counts
3 → 36
Calls

3 calls:

369.0ms
(/.f64 (log.f64 (/.f64 (+.f64 1 x) x)) n)
4.0ms
(log.f64 (/.f64 (+.f64 1 x) x))
2.0ms
(/.f64 (+.f64 1 x) x)

rewrite18.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64
36×times-frac_binary64
29×add-sqr-sqrt_binary64
29×add-cube-cbrt_binary64
16×log-prod_binary64
Counts
3 → 98
Calls

3 calls:

6.0ms
(/.f64 (log.f64 (/.f64 (+.f64 1 x) x)) n)
4.0ms
(/.f64 (+.f64 1 x) x)
3.0ms
(log.f64 (/.f64 (+.f64 1 x) x))

simplify105.0ms (0.6%)

Algorithm
egg-herbie
Rules
632×fma-neg_binary64
552×distribute-rgt-in_binary64
325×cancel-sign-sub-inv_binary64
272×sub-neg_binary64
226×associate-/r*_binary64
Counts
134 → 184
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01902142
14162029
210952005
329151974
449581974
551511974

prune190.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1822184
Fresh2810
Picked101
Done000
Total18510195
Error
0.1b
Counts
195 → 10
Alt Table
StatusErrorProgram
38.5b
(/.f64 (+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))) n)
20.1b
(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (*.f64 n (+.f64 (*.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (*.f64 (log.f64 x) (log.f64 x)) (*.f64 (log1p.f64 x) (log.f64 x))))))
19.7b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (-.f64 (log1p.f64 x) (log.f64 x))) (-.f64 (log1p.f64 x) (log.f64 x)))) n)
19.6b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
24.7b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
19.6b
(*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) n))
19.5b
(/.f64 1 (/.f64 n (log.f64 (/.f64 (+.f64 1 x) x))))
20.3b
(/.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 x)))) n)
31.1b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
36.1b
(-.f64 (+.f64 (+.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n)) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (*.f64 x x) (*.f64 n n))) (fma.f64 1/24 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (pow.f64 x 4) (pow.f64 n 4))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 3)) (+.f64 (/.f64 1/3 n) (/.f64 1/6 (pow.f64 n 3))))))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 4)) (-.f64 (/.f64 11/24 (*.f64 n n)) (/.f64 1/4 (pow.f64 n 3))))) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 n (*.f64 n (pow.f64 x 3)))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) n) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4))))))
Compiler

Compiled 3404 to 1958 computations (42.5% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 1 x) x)
0.2b
(/.f64 n (log.f64 (/.f64 (+.f64 1 x) x)))
0.2b
(/.f64 1 (/.f64 n (log.f64 (/.f64 (+.f64 1 x) x))))
4.4b
(log.f64 (/.f64 (+.f64 1 x) x))

series663.0ms (4%)

Counts
2 → 36
Calls

2 calls:

336.0ms
(/.f64 n (log.f64 (/.f64 (+.f64 1 x) x)))
327.0ms
(/.f64 1 (/.f64 n (log.f64 (/.f64 (+.f64 1 x) x))))

rewrite21.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
108×times-frac_binary64
60×*-un-lft-identity_binary64
60×add-sqr-sqrt_binary64
60×add-cube-cbrt_binary64
20×associate-/r*_binary64
Counts
2 → 123
Calls

2 calls:

7.0ms
(/.f64 n (log.f64 (/.f64 (+.f64 1 x) x)))
5.0ms
(/.f64 1 (/.f64 n (log.f64 (/.f64 (+.f64 1 x) x))))

simplify134.0ms (0.8%)

Algorithm
egg-herbie
Rules
382×times-frac_binary64
370×sub-neg_binary64
327×associate-/l*_binary64
306×associate-/r*_binary64
303×div-sub_binary64
Counts
159 → 195
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01743614
14043123
211623060
340223058
448813058
554633058

prune345.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3101311
Fresh099
Picked011
Done000
Total31011321
Error
0.1b
Counts
321 → 11
Alt Table
StatusErrorProgram
38.0b
(/.f64 1 (fma.f64 n 1/2 (fma.f64 x n (*.f64 (/.f64 n x) (+.f64 (/.f64 1/24 x) -1/12)))))
38.5b
(/.f64 (+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))) n)
20.1b
(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (*.f64 n (+.f64 (*.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (*.f64 (log.f64 x) (log.f64 x)) (*.f64 (log1p.f64 x) (log.f64 x))))))
19.7b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (-.f64 (log1p.f64 x) (log.f64 x))) (-.f64 (log1p.f64 x) (log.f64 x)))) n)
19.6b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
24.7b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
19.6b
(*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) n))
19.5b
(/.f64 1 (/.f64 n (log.f64 (/.f64 (+.f64 1 x) x))))
20.3b
(/.f64 (+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 x)))) n)
31.1b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
36.1b
(-.f64 (+.f64 (+.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n)) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (*.f64 x x) (*.f64 n n))) (fma.f64 1/24 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 (pow.f64 x 4) (pow.f64 n 4))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 3)) (+.f64 (/.f64 1/3 n) (/.f64 1/6 (pow.f64 n 3))))))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (pow.f64 x 4)) (-.f64 (/.f64 11/24 (*.f64 n n)) (/.f64 1/4 (pow.f64 n 3))))) (fma.f64 1/2 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 n (*.f64 n (pow.f64 x 3)))) (*.f64 (/.f64 (exp.f64 (/.f64 (log.f64 x) n)) n) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4))))))
Compiler

Compiled 6124 to 3708 computations (39.5% saved)

regimes3.4s (20.6%)

Accuracy

Total 8.0b remaining (98.2%)

Threshold costs 0b (0%)

Counts
209 → 4
Compiler

Compiled 15738 to 10589 computations (32.7% saved)

bsearch279.0ms (1.7%)

Steps
ItersRangePoint
6
1684.0842453015853
9641.706934196658
3872.7799695531517
6
3.7520093999910654e-206
4.180075642702265e-205
3.820976062708217e-206
7
5.117666865397309e-227
9.515439853571591e-225
8.40015892724182e-225
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify10.0ms (0.1%)

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
041117
152117
259117
363117
465117
564117

end203.0ms (1.2%)

Compiler

Compiled 479 to 278 computations (42% saved)

Profiling

Loading profile data...