Details

Time bar (total: 15.2s)

analyze1.0s (6.6%)

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)

sample9.5s (62.6%)

Results
2.4s2806×body1024valid
2.2s1731×body1024invalid
1.8s1863×body2048valid
1.4s1005×body512invalid
710.0ms1220×body512valid
335.0ms1770×body128valid
222.0ms509×body256invalid
218.0ms597×body256valid
205.0ms1150×body128invalid
8.0msbody2048invalid
Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify53.0ms (0.3%)

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
30.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
30.9b
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
Compiler

Compiled 45 to 33 computations (26.7% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
2.2b
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series34.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

34.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite19.0ms (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:

9.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify179.0ms (1.2%)

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

prune199.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1384142
Fresh000
Picked101
Done000
Total1394143
Error
1.0b
Counts
143 → 4
Alt Table
StatusErrorProgram
16.9b
(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
30.4b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
39.9b
(-.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))))))
24.9b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 4) (pow.f64 n 4))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n)))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4))) (/.f64 (log.f64 x) n)))))
Compiler

Compiled 6570 to 4504 computations (31.4% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
3.3b
(-.f64 (log1p.f64 x) (log.f64 x))

series544.0ms (3.6%)

Counts
2 → 36
Calls

2 calls:

541.0ms
(/.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))

simplify128.0ms (0.8%)

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

prune117.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1108118
Fresh033
Picked101
Done000
Total11111122
Error
0.0b
Counts
122 → 11
Alt Table
StatusErrorProgram
39.9b
(-.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))))))
17.2b
(/.f64 (expm1.f64 (log1p.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) n)
32.9b
(/.f64 (-.f64 (-.f64 (log1p.f64 x) (*.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (cbrt.f64 x))) n)
17.0b
(*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) n))
30.4b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
38.5b
(/.f64 (fma.f64 (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x))) (cbrt.f64 (log1p.f64 x)) (neg.f64 (log.f64 x))) n)
42.6b
(/.f64 (-.f64 (+.f64 (/.f64 1 x) (/.f64 1/3 (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4)))) n)
17.0b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) n)
16.9b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
17.0b
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
24.9b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 4) (pow.f64 n 4))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n)))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4))) (/.f64 (log.f64 x) n)))))
Compiler

Compiled 2628 to 1024 computations (61% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
3.3b
(-.f64 (log1p.f64 x) (log.f64 x))

series475.0ms (3.1%)

Counts
1 → 24
Calls

1 calls:

475.0ms
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
13×associate-*r*_binary64
13×*-un-lft-identity_binary64
11×times-frac_binary64
10×add-exp-log_binary64
Counts
1 → 45
Calls

1 calls:

12.0ms
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))

simplify74.0ms (0.5%)

Algorithm
egg-herbie
Rules
763×fma-def_binary64
436×times-frac_binary64
422×fma-neg_binary64
209×distribute-rgt-neg-out_binary64
208×associate-*l*_binary64
Counts
69 → 83
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01251178
13021086
28381086
321981086
449001086
551101086

prune136.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1363139
Fresh3710
Picked011
Done000
Total13911150
Error
0.0b
Counts
150 → 11
Alt Table
StatusErrorProgram
17.1b
(*.f64 (cbrt.f64 (pow.f64 (-.f64 (log1p.f64 x) (log.f64 x)) 3)) (/.f64 1 n))
17.0b
(*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) n))
30.4b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
38.5b
(/.f64 (fma.f64 (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x))) (cbrt.f64 (log1p.f64 x)) (neg.f64 (log.f64 x))) n)
42.6b
(*.f64 (-.f64 (+.f64 (/.f64 1 x) (/.f64 1/3 (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4)))) (/.f64 1 n))
39.9b
(-.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))))))
17.2b
(*.f64 (expm1.f64 (log1p.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 1 n))
17.0b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) n)
16.9b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
17.0b
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
24.9b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 4) (pow.f64 n 4))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n)))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4))) (/.f64 (log.f64 x) n)))))
Compiler

Compiled 3111 to 1375 computations (55.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))
0.3b
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
3.3b
(-.f64 (log1p.f64 x) (log.f64 x))

series990.0ms (6.5%)

Counts
2 → 48
Calls

2 calls:

504.0ms
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
486.0ms
(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))

rewrite29.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
162×times-frac_binary64
126×*-un-lft-identity_binary64
110×add-sqr-sqrt_binary64
78×add-cube-cbrt_binary64
32×distribute-lft-out--_binary64
Counts
2 → 165
Calls

2 calls:

8.0ms
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
4.0ms
(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))

simplify140.0ms (0.9%)

Algorithm
egg-herbie
Rules
395×times-frac_binary64
339×associate-/l*_binary64
331×fma-neg_binary64
326×associate-/r*_binary64
324×fma-def_binary64
Counts
213 → 211
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02134642
14884291
214454175
343534175
449924175

prune249.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2670267
Fresh099
Picked011
Done011
Total26711278
Error
0.0b
Counts
278 → 11
Alt Table
StatusErrorProgram
17.1b
(*.f64 (cbrt.f64 (pow.f64 (-.f64 (log1p.f64 x) (log.f64 x)) 3)) (/.f64 1 n))
17.0b
(*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) n))
30.4b
(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (exp.f64 (/.f64 (log.f64 x) n)))
38.5b
(/.f64 (fma.f64 (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x))) (cbrt.f64 (log1p.f64 x)) (neg.f64 (log.f64 x))) n)
42.6b
(*.f64 (-.f64 (+.f64 (/.f64 1 x) (/.f64 1/3 (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4)))) (/.f64 1 n))
39.9b
(-.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))))))
17.2b
(*.f64 (expm1.f64 (log1p.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 1 n))
17.0b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) n)
16.9b
(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
17.0b
(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
24.9b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 4) (pow.f64 n 4))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n)))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4))) (/.f64 (log.f64 x) n)))))
Compiler

Compiled 5588 to 1964 computations (64.9% saved)

regimes990.0ms (6.5%)

Accuracy

Total 10.8b remaining (98.9%)

Threshold costs 0b (0%)

Counts
137 → 3
Compiler

Compiled 11675 to 7774 computations (33.4% saved)

bsearch5.0ms (0%)

Compiler

Compiled 5 to 4 computations (20% 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
03167
13967
24567
35067
45467
55567
65467

end251.0ms (1.7%)

Compiler

Compiled 434 to 284 computations (34.6% saved)

Profiling

Loading profile data...