Details

Time bar (total: 1.7min)

analyze198.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%0%50%4
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample39.0ms (0%)

Algorithm
intervals
Results
14.0ms62×body1024valid
9.0ms133×body128valid
5.0ms34×body512valid
4.0ms11×body2048valid
1.0ms16×body256valid
Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify97.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
07111
17111

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.5b
Counts
2 → 1
Compiler

Compiled 7 to 6 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

3.4b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.8b
(log.f64 (+.f64 N 1))
2.8b
(log.f64 (+.f64 N 1))
3.4b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite15.0ms (0%)

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity_binary64_78
11×log-prod_binary64_164
add-sqr-sqrt_binary64_100 pow1_binary64_139
add-cube-cbrt_binary64_113 log-pow_binary64_167
distribute-lft-out--_binary64_30 associate--l+_binary64_15 log-div_binary64_165 cancel-sign-sub-inv_binary64_44
associate--r+_binary64_14 add-exp-log_binary64_116
add-cbrt-cube_binary64_114 add-log-exp_binary64_117 flip-+_binary64_52 distribute-lft-out_binary64_29 associate--l-_binary64_16 flip3-+_binary64_81
flip3--_binary64_82 diff-log_binary64_170 flip--_binary64_53 rem-log-exp_binary64_119 difference-of-squares_binary64_47 sub-neg_binary64_71
Counts
2 → 44
Calls

4 calls:

8.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms
(log.f64 (+.f64 N 1))
0.0ms
(log.f64 (+.f64 N 1))
0.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

series88.0ms (0.1%)

Counts
2 → 21
Calls

2 calls:

59.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
28.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 296 to 255 computations (13.9% saved)

simplify85.0ms (0.1%)

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
04924853
14924853

prune261.0ms (0.3%)

Pruning

40 alts after pruning (39 fresh and 1 done)

PrunedKeptTotal
New263965
Fresh000
Picked000
Done011
Total264066
Error
0.0b
Counts
66 → 40
Compiler

Compiled 1126 to 790 computations (29.8% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

3.3b
(log.f64 (/.f64 (+.f64 N 1) N))
0.0b
(/.f64 (+.f64 N 1) N)
0.0b
(/.f64 (+.f64 N 1) N)
3.3b
(log.f64 (/.f64 (+.f64 N 1) N))

rewrite14.0ms (0%)

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity_binary64_78
24×times-frac_binary64_84
19×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
16×log-prod_binary64_164
add-exp-log_binary64_116 distribute-lft-out_binary64_29
add-cbrt-cube_binary64_114 associate-/l*_binary64_23
associate-/r*_binary64_22 pow1_binary64_139
add-log-exp_binary64_117 div-exp_binary64_129 div-inv_binary64_75 rem-log-exp_binary64_119 associate-/l/_binary64_25
cbrt-undiv_binary64_112 flip-+_binary64_52 frac-2neg_binary64_89 log-div_binary64_165 clear-num_binary64_77 log-pow_binary64_167 flip3-+_binary64_81
Counts
2 → 60
Calls

4 calls:

5.0ms
(/.f64 (+.f64 N 1) N)
5.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
0.0ms
(/.f64 (+.f64 N 1) N)
0.0ms
(log.f64 (/.f64 (+.f64 N 1) N))

series84.0ms (0.1%)

Counts
2 → 18
Calls

2 calls:

49.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
34.0ms
(/.f64 (+.f64 N 1) N)
Compiler

Compiled 198 to 182 computations (8.1% saved)

simplify66.0ms (0.1%)

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
053301074

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 N (-.f64 1/3 (*.f64 N 1/4)))
0.1b
(*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))
0.0b
(-.f64 1/3 (*.f64 N 1/4))
0.0b
(-.f64 (+.f64 N (*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))) (log.f64 N))
0.0b
(-.f64 (+.f64 N (*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))) (log.f64 N))
0.0b
(-.f64 1/3 (*.f64 N 1/4))
0.1b
(*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))
0.2b
(*.f64 N (-.f64 1/3 (*.f64 N 1/4)))

rewrite39.0ms (0%)

Algorithm
rewrite-expression-head
Rules
17×cancel-sign-sub-inv_binary64_44
16×add-sqr-sqrt_binary64_100
14×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 *-un-lft-identity_binary64_78
13×pow1_binary64_139
11×add-cbrt-cube_binary64_114 add-cube-cbrt_binary64_113 add-exp-log_binary64_116
10×sub-neg_binary64_71
add-log-exp_binary64_117 associate--l+_binary64_15
associate-*r*_binary64_18
associate-*l*_binary64_19 cbrt-unprod_binary64_111 prod-exp_binary64_127 flip3--_binary64_82 flip--_binary64_53 pow-prod-down_binary64_149 associate-*r/_binary64_20
diff-log_binary64_170 associate--r+_binary64_14 log-prod_binary64_164
*-commutative_binary64_9 distribute-lft-out--_binary64_30 unswap-sqr_binary64_46 log-pow_binary64_167
difference-of-squares_binary64_47 sum-log_binary64_169
Counts
4 → 96
Calls

8 calls:

12.0ms
(*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))
7.0ms
(-.f64 (+.f64 N (*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))) (log.f64 N))
6.0ms
(*.f64 N (-.f64 1/3 (*.f64 N 1/4)))
6.0ms
(-.f64 1/3 (*.f64 N 1/4))
0.0ms
(-.f64 (+.f64 N (*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))) (log.f64 N))

series153.0ms (0.1%)

Counts
4 → 25
Calls

4 calls:

47.0ms
(*.f64 N (-.f64 1/3 (*.f64 N 1/4)))
38.0ms
(*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))
34.0ms
(-.f64 (+.f64 N (*.f64 (*.f64 N N) (-.f64 (*.f64 N (-.f64 1/3 (*.f64 N 1/4))) 1/2))) (log.f64 N))
34.0ms
(-.f64 1/3 (*.f64 N 1/4))
Compiler

Compiled 542 to 421 computations (22.3% saved)

simplify70.0ms (0.1%)

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
051002176

localize13.0ms (0%)

Local error

Found 6 expressions with local error:

16.0b
(log.f64 (-.f64 (*.f64 N N) (*.f64 1 1)))
3.4b
(-.f64 (log.f64 (-.f64 (*.f64 N N) (*.f64 1 1))) (+.f64 (log.f64 N) (log.f64 (+.f64 N -1))))
0.0b
(+.f64 (log.f64 N) (log.f64 (+.f64 N -1)))
0.0b
(+.f64 (log.f64 N) (log.f64 (+.f64 N -1)))
3.4b
(-.f64 (log.f64 (-.f64 (*.f64 N N) (*.f64 1 1))) (+.f64 (log.f64 N) (log.f64 (+.f64 N -1))))
16.0b
(log.f64 (-.f64 (*.f64 N N) (*.f64 1 1)))

rewrite34.0ms (0%)

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity_binary64_78
25×pow1_binary64_139
22×log-pow_binary64_167
17×distribute-lft-out_binary64_29
16×log-prod_binary64_164
11×add-sqr-sqrt_binary64_100
10×distribute-lft-out--_binary64_30
add-cube-cbrt_binary64_113 log-div_binary64_165
cancel-sign-sub-inv_binary64_44
associate-+r+_binary64_10
add-log-exp_binary64_117 associate-+r-_binary64_12 associate--l+_binary64_15 add-exp-log_binary64_116
add-cbrt-cube_binary64_114 flip-+_binary64_52 flip3--_binary64_82 associate-+l+_binary64_11 flip--_binary64_53 difference-of-squares_binary64_47 flip3-+_binary64_81
diff-log_binary64_170 associate--r-_binary64_17 associate--l-_binary64_16 sum-log_binary64_169
+-commutative_binary64_8 associate--r+_binary64_14 rem-log-exp_binary64_119 sub-neg_binary64_71 difference-of-sqr--1_binary64_49
Counts
3 → 79
Calls

6 calls:

15.0ms
(-.f64 (log.f64 (-.f64 (*.f64 N N) (*.f64 1 1))) (+.f64 (log.f64 N) (log.f64 (+.f64 N -1))))
7.0ms
(+.f64 (log.f64 N) (log.f64 (+.f64 N -1)))
5.0ms
(log.f64 (-.f64 (*.f64 N N) (*.f64 1 1)))
0.0ms
(+.f64 (log.f64 N) (log.f64 (+.f64 N -1)))
0.0ms
(-.f64 (log.f64 (-.f64 (*.f64 N N) (*.f64 1 1))) (+.f64 (log.f64 N) (log.f64 (+.f64 N -1))))

series134.0ms (0.1%)

Counts
3 → 21
Calls

3 calls:

58.0ms
(-.f64 (log.f64 (-.f64 (*.f64 N N) (*.f64 1 1))) (+.f64 (log.f64 N) (log.f64 (+.f64 N -1))))
39.0ms
(log.f64 (-.f64 (*.f64 N N) (*.f64 1 1)))
36.0ms
(+.f64 (log.f64 N) (log.f64 (+.f64 N -1)))
Compiler

Compiled 439 to 382 computations (13% saved)

simplify85.0ms (0.1%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
051011524

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

2.8b
(log.f64 (+.f64 N 1))
0.2b
(*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1))))
0.1b
(sqrt.f64 (log.f64 (+.f64 N 1)))
0.1b
(sqrt.f64 (log.f64 (+.f64 N 1)))
0.2b
(*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1))))
2.8b
(log.f64 (+.f64 N 1))
2.8b
(log.f64 (+.f64 N 1))
15.7b
(-.f64 (*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))

rewrite34.0ms (0%)

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt_binary64_100
28×pow1_binary64_139
26×sqrt-prod_binary64_94
22×*-un-lft-identity_binary64_78
16×add-cube-cbrt_binary64_113
11×swap-sqr_binary64_45 log-prod_binary64_164
log-pow_binary64_167
sqrt-pow1_binary64_96 add-exp-log_binary64_116 pow1/2_binary64_158
associate-*l*_binary64_19 associate-*r*_binary64_18
add-cbrt-cube_binary64_114
add-log-exp_binary64_117 pow-prod-up_binary64_148
unswap-sqr_binary64_46 log-div_binary64_165 cancel-sign-sub-inv_binary64_44
pow-sqr_binary64_51 associate--r+_binary64_14 pow-prod-down_binary64_149
flip-+_binary64_52 rem-sqrt-square_binary64_91 rem-log-exp_binary64_119 distribute-lft-out_binary64_29 flip3-+_binary64_81
pow2_binary64_159 *-commutative_binary64_9 sqr-abs_binary64_93 cbrt-unprod_binary64_111 prod-exp_binary64_127 flip3--_binary64_82 diff-log_binary64_170 sqrt-unprod_binary64_98 flip--_binary64_53 rem-square-sqrt_binary64_90 difference-of-squares_binary64_47 pow-plus_binary64_141 sub-neg_binary64_71
Counts
4 → 104
Calls

8 calls:

8.0ms
(*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1))))
7.0ms
(-.f64 (*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
3.0ms
(log.f64 (+.f64 N 1))
3.0ms
(log.f64 (+.f64 N 1))
0.0ms
(sqrt.f64 (log.f64 (+.f64 N 1)))

series153.0ms (0.1%)

Counts
4 → 39
Calls

4 calls:

57.0ms
(-.f64 (*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
33.0ms
(log.f64 (+.f64 N 1))
31.0ms
(log.f64 (+.f64 N 1))
30.0ms
(*.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) (sqrt.f64 (log.f64 (+.f64 N 1))))
Compiler

Compiled 720 to 613 computations (14.9% saved)

simplify112.0ms (0.1%)

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (88.0ms)

IterNodesCost
048911584
148911584

prune4.8s (4.7%)

Pruning

181 alts after pruning (176 fresh and 5 done)

PrunedKeptTotal
New291151442
Fresh92534
Picked000
Done156
Total301181482
Error
0.0b
Counts
482 → 181
Compiler

Compiled 8614 to 5986 computations (30.5% saved)

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

3.3b
(log.f64 (/.f64 1 (/.f64 N (+.f64 N 1))))
0.0b
(/.f64 N (+.f64 N 1))
0.0b
(/.f64 1 (/.f64 N (+.f64 N 1)))
0.0b
(/.f64 1 (/.f64 N (+.f64 N 1)))
0.0b
(/.f64 N (+.f64 N 1))
3.3b
(log.f64 (/.f64 1 (/.f64 N (+.f64 N 1))))

rewrite48.0ms (0%)

Algorithm
rewrite-expression-head
Rules
204×times-frac_binary64_84
156×*-un-lft-identity_binary64_78
106×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
59×log-prod_binary64_164
28×add-exp-log_binary64_116
25×distribute-lft-out_binary64_29
22×associate-/r*_binary64_22
18×associate-/r/_binary64_24
15×div-exp_binary64_129
10×add-cbrt-cube_binary64_114 div-inv_binary64_75
flip-+_binary64_52 flip3-+_binary64_81
rem-log-exp_binary64_119
associate-/l*_binary64_23 pow1_binary64_139
cbrt-undiv_binary64_112 1-exp_binary64_122 rec-exp_binary64_128
add-log-exp_binary64_117 log-pow_binary64_167
inv-pow_binary64_163 frac-2neg_binary64_89 pow-flip_binary64_152 clear-num_binary64_77
log-rec_binary64_166 log-div_binary64_165
Counts
3 → 207
Calls

6 calls:

10.0ms
(log.f64 (/.f64 1 (/.f64 N (+.f64 N 1))))
9.0ms
(/.f64 1 (/.f64 N (+.f64 N 1)))
5.0ms
(/.f64 N (+.f64 N 1))
0.0ms
(/.f64 1 (/.f64 N (+.f64 N 1)))
0.0ms
(/.f64 N (+.f64 N 1))

series114.0ms (0.1%)

Counts
3 → 30
Calls

3 calls:

46.0ms
(log.f64 (/.f64 1 (/.f64 N (+.f64 N 1))))
38.0ms
(/.f64 1 (/.f64 N (+.f64 N 1)))
30.0ms
(/.f64 N (+.f64 N 1))
Compiler

Compiled 330 to 304 computations (7.9% saved)

simplify131.0ms (0.1%)

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
049914047
149914047

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.6b
(/.f64 1/2 (*.f64 N N))
0.0b
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
0.0b
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
0.6b
(/.f64 1/2 (*.f64 N N))

rewrite20.0ms (0%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64_100
13×times-frac_binary64_84
11×*-un-lft-identity_binary64_78
add-cbrt-cube_binary64_114 add-exp-log_binary64_116 cancel-sign-sub-inv_binary64_44
add-cube-cbrt_binary64_113 difference-of-squares_binary64_47
add-log-exp_binary64_117
div-inv_binary64_75 associate-/l*_binary64_23
cbrt-undiv_binary64_112 div-exp_binary64_129 distribute-lft-out--_binary64_30 pow1_binary64_139
cbrt-unprod_binary64_111 prod-exp_binary64_127 frac-sub_binary64_87 flip3--_binary64_82 diff-log_binary64_170 frac-2neg_binary64_89 flip--_binary64_53 associate-/r*_binary64_22 clear-num_binary64_77 sub-neg_binary64_71
Counts
2 → 48
Calls

4 calls:

11.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
4.0ms
(/.f64 1/2 (*.f64 N N))
0.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
0.0ms
(/.f64 1/2 (*.f64 N N))

series65.0ms (0.1%)

Counts
2 → 9
Calls

2 calls:

39.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
27.0ms
(/.f64 1/2 (*.f64 N N))
Compiler

Compiled 131 to 119 computations (9.2% saved)

simplify93.0ms (0.1%)

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
04864753
14864753

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

15.9b
(log.f64 (/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N)))
0.4b
(/.f64 (+.f64 N 1) (sqrt.f64 N))
0.2b
(/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N))
0.2b
(/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N))
0.4b
(/.f64 (+.f64 N 1) (sqrt.f64 N))
15.9b
(log.f64 (/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N)))

rewrite102.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
672×times-frac_binary64_84
500×*-un-lft-identity_binary64_78
342×sqrt-prod_binary64_94
330×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
172×log-prod_binary64_164
85×distribute-lft-out_binary64_29
32×associate-/l*_binary64_23
16×div-inv_binary64_75 add-exp-log_binary64_116
12×associate-/r*_binary64_22
10×add-cbrt-cube_binary64_114
div-exp_binary64_129
cbrt-undiv_binary64_112 pow1_binary64_139
add-log-exp_binary64_117 rem-log-exp_binary64_119 associate-/l/_binary64_25
frac-2neg_binary64_89 clear-num_binary64_77
flip-+_binary64_52 log-div_binary64_165 log-pow_binary64_167 flip3-+_binary64_81
Counts
3 → 449
Calls

6 calls:

20.0ms
(/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N))
18.0ms
(log.f64 (/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N)))
6.0ms
(/.f64 (+.f64 N 1) (sqrt.f64 N))
0.0ms
(/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N))
0.0ms
(/.f64 (+.f64 N 1) (sqrt.f64 N))

series91.0ms (0.1%)

Counts
3 → 17
Calls

3 calls:

49.0ms
(log.f64 (/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N)))
27.0ms
(/.f64 (/.f64 (+.f64 N 1) (sqrt.f64 N)) (sqrt.f64 N))
15.0ms
(/.f64 (+.f64 N 1) (sqrt.f64 N))
Compiler

Compiled 238 to 211 computations (11.3% saved)

simplify210.0ms (0.2%)

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
0494812208
1494812208

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N))) (cbrt.f64 (/.f64 (+.f64 N 1) N)))
0.0b
(/.f64 (+.f64 N 1) N)
0.0b
(/.f64 (+.f64 N 1) N)
0.0b
(/.f64 (+.f64 N 1) N)
0.2b
(cbrt.f64 (/.f64 (+.f64 N 1) N))
0.2b
(cbrt.f64 (/.f64 (+.f64 N 1) N))
0.3b
(*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N)))
3.3b
(log.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N))) (cbrt.f64 (/.f64 (+.f64 N 1) N))))

rewrite81.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
120×cbrt-prod_binary64_109
114×*-un-lft-identity_binary64_78
90×times-frac_binary64_84
84×add-sqr-sqrt_binary64_100
60×add-cube-cbrt_binary64_113
31×pow1_binary64_139
25×swap-sqr_binary64_45
24×distribute-lft-out_binary64_29
19×associate-*l*_binary64_19 associate-*r*_binary64_18
18×cbrt-div_binary64_110
17×pow1/3_binary64_160
15×log-pow_binary64_167
12×add-exp-log_binary64_116
11×pow-prod-up_binary64_148
unswap-sqr_binary64_46
pow-prod-down_binary64_149 log-div_binary64_165 pow-plus_binary64_141
div-inv_binary64_75 frac-times_binary64_88 associate-*l/_binary64_21
pow-sqr_binary64_51
add-cbrt-cube_binary64_114 add-log-exp_binary64_117 prod-exp_binary64_127 associate-*r/_binary64_20
pow2_binary64_159 rem-log-exp_binary64_119
*-commutative_binary64_9 cbrt-unprod_binary64_111 log-prod_binary64_164 pow3_binary64_161
Counts
4 → 176
Calls

8 calls:

23.0ms
(*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N)))
21.0ms
(log.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N))) (cbrt.f64 (/.f64 (+.f64 N 1) N))))
11.0ms
(cbrt.f64 (/.f64 (+.f64 N 1) N))
5.0ms
(cbrt.f64 (/.f64 (+.f64 N 1) N))
0.0ms
(/.f64 (+.f64 N 1) N)

series250.0ms (0.2%)

Counts
4 → 42
Calls

4 calls:

80.0ms
(*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N)))
68.0ms
(log.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) (cbrt.f64 (/.f64 (+.f64 N 1) N))) (cbrt.f64 (/.f64 (+.f64 N 1) N))))
52.0ms
(cbrt.f64 (/.f64 (+.f64 N 1) N))
50.0ms
(cbrt.f64 (/.f64 (+.f64 N 1) N))
Compiler

Compiled 1016 to 874 computations (14% saved)

simplify98.0ms (0.1%)

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049274387
149274387

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1))))
0.1b
(sqrt.f64 (log.f64 (+.f64 N 1)))
0.1b
(sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1))))
0.0b
(-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))
0.2b
(*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1))))
2.8b
(log.f64 (+.f64 N 1))
15.7b
(-.f64 (*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
16.0b
(log.f64 (+.f64 -1 (*.f64 N N)))

rewrite37.0ms (0%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64_100
18×*-un-lft-identity_binary64_78
16×sqrt-prod_binary64_94 pow1_binary64_139
12×add-cube-cbrt_binary64_113
11×associate-*l*_binary64_19
10×log-prod_binary64_164
add-exp-log_binary64_116 log-pow_binary64_167
associate-*r*_binary64_18
add-cbrt-cube_binary64_114
add-log-exp_binary64_117
distribute-lft-out--_binary64_30 unswap-sqr_binary64_46 log-div_binary64_165 cancel-sign-sub-inv_binary64_44
associate--r+_binary64_14 pow-prod-down_binary64_149
sqrt-pow1_binary64_96 flip-+_binary64_52 flip3--_binary64_82 flip--_binary64_53 associate-*l/_binary64_21 rem-log-exp_binary64_119 sqrt-div_binary64_95 pow1/2_binary64_158 flip3-+_binary64_81
*-commutative_binary64_9 cbrt-unprod_binary64_111 prod-exp_binary64_127 diff-log_binary64_170 sqrt-unprod_binary64_98 difference-of-squares_binary64_47 distribute-lft-out_binary64_29 sub-neg_binary64_71
Counts
4 → 85
Calls

8 calls:

11.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1))))
11.0ms
(-.f64 (*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
3.0ms
(log.f64 (+.f64 -1 (*.f64 N N)))
3.0ms
(log.f64 (+.f64 N 1))
0.0ms
(-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))

series202.0ms (0.2%)

Counts
4 → 24
Calls

4 calls:

69.0ms
(-.f64 (*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
63.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 -1 (*.f64 N N))) (log.f64 (+.f64 N -1)))) (sqrt.f64 (log.f64 (+.f64 N 1))))
41.0ms
(log.f64 (+.f64 -1 (*.f64 N N)))
28.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 698 to 592 computations (15.2% saved)

simplify93.0ms (0.1%)

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049232589
149232589

prune21.2s (20.5%)

Pruning

455 alts after pruning (447 fresh and 8 done)

PrunedKeptTotal
New7813061087
Fresh30141171
Picked000
Done2810
Total8134551268
Error
0.0b
Counts
1268 → 455
Compiler

Compiled 21983 to 15715 computations (28.5% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

3.3b
(log.f64 (/.f64 N (+.f64 N 1)))
0.0b
(/.f64 N (+.f64 N 1))
0.0b
(/.f64 N (+.f64 N 1))
3.3b
(log.f64 (/.f64 N (+.f64 N 1)))

rewrite15.0ms (0%)

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity_binary64_78
24×times-frac_binary64_84
19×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
18×log-prod_binary64_164
add-exp-log_binary64_116 distribute-lft-out_binary64_29
add-cbrt-cube_binary64_114 associate-/r*_binary64_22 associate-/r/_binary64_24
associate-/l*_binary64_23 pow1_binary64_139
add-log-exp_binary64_117 div-exp_binary64_129 flip-+_binary64_52 div-inv_binary64_75 rem-log-exp_binary64_119 flip3-+_binary64_81
cbrt-undiv_binary64_112 frac-2neg_binary64_89 log-div_binary64_165 clear-num_binary64_77 log-pow_binary64_167
Counts
2 → 62
Calls

4 calls:

5.0ms
(/.f64 N (+.f64 N 1))
5.0ms
(log.f64 (/.f64 N (+.f64 N 1)))
0.0ms
(/.f64 N (+.f64 N 1))
0.0ms
(log.f64 (/.f64 N (+.f64 N 1)))

series80.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

52.0ms
(log.f64 (/.f64 N (+.f64 N 1)))
28.0ms
(/.f64 N (+.f64 N 1))
Compiler

Compiled 332 to 304 computations (8.4% saved)

simplify69.0ms (0.1%)

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049991208
149991208

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.6b
(/.f64 -1/2 (*.f64 N N))
0.6b
(/.f64 -1/2 (*.f64 N N))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64_114 add-exp-log_binary64_116
add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 times-frac_binary64_84 associate-/l*_binary64_23 *-un-lft-identity_binary64_78
cbrt-undiv_binary64_112 div-exp_binary64_129
add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 frac-2neg_binary64_89 div-inv_binary64_75 associate-/r*_binary64_22 clear-num_binary64_77 pow1_binary64_139
Counts
1 → 21
Calls

2 calls:

4.0ms
(/.f64 -1/2 (*.f64 N N))
0.0ms
(/.f64 -1/2 (*.f64 N N))

series24.0ms (0%)

Counts
1 → 3
Calls

1 calls:

24.0ms
(/.f64 -1/2 (*.f64 N N))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify90.0ms (0.1%)

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
04675212
14675212

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

15.7b
(-.f64 (pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2) (log.f64 N))
2.8b
(log.f64 (+.f64 N 1))
0.2b
(pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2)
0.1b
(sqrt.f64 (log.f64 (+.f64 N 1)))
0.1b
(sqrt.f64 (log.f64 (+.f64 N 1)))
0.2b
(pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2)
2.8b
(log.f64 (+.f64 N 1))
15.7b
(-.f64 (pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2) (log.f64 N))

rewrite23.0ms (0%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64_100
16×*-un-lft-identity_binary64_78
12×pow1_binary64_139
11×add-cube-cbrt_binary64_113
sqrt-prod_binary64_94 unpow-prod-down_binary64_157
log-prod_binary64_164
add-exp-log_binary64_116
add-log-exp_binary64_117 difference-of-squares_binary64_47 log-pow_binary64_167
add-cbrt-cube_binary64_114 cancel-sign-sub-inv_binary64_44
associate--r+_binary64_14 pow-pow_binary64_150 pow-unpow_binary64_155
sqrt-pow1_binary64_96 distribute-lft-out--_binary64_30 unpow2_binary64_143 sqr-pow_binary64_50 log-div_binary64_165 pow1/2_binary64_158
sqrt-pow2_binary64_97 pow-exp_binary64_146 pow-to-exp_binary64_147 flip-+_binary64_52 rem-sqrt-square_binary64_91 flip3--_binary64_82 diff-log_binary64_170 flip--_binary64_53 rem-log-exp_binary64_119 distribute-lft-out_binary64_29 sub-neg_binary64_71 flip3-+_binary64_81
Counts
4 → 79
Calls

8 calls:

10.0ms
(-.f64 (pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2) (log.f64 N))
3.0ms
(pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2)
3.0ms
(log.f64 (+.f64 N 1))
1.0ms
(sqrt.f64 (log.f64 (+.f64 N 1)))
0.0ms
(sqrt.f64 (log.f64 (+.f64 N 1)))

series211.0ms (0.2%)

Counts
4 → 33
Calls

4 calls:

59.0ms
(pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2)
59.0ms
(sqrt.f64 (log.f64 (+.f64 N 1)))
57.0ms
(-.f64 (pow.f64 (sqrt.f64 (log.f64 (+.f64 N 1))) 2) (log.f64 N))
36.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 739 to 645 computations (12.7% saved)

simplify67.0ms (0.1%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049171497
149171497

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(cbrt.f64 (+.f64 N 1))
0.2b
(+.f64 (*.f64 2 (log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))) (log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N))))
0.1b
(/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N))
0.1b
(/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N))
0.6b
(cbrt.f64 N)
0.6b
(cbrt.f64 N)
3.3b
(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))
3.3b
(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))

rewrite34.0ms (0%)

Algorithm
rewrite-expression-head
Rules
96×cbrt-prod_binary64_109
92×log-prod_binary64_164
84×times-frac_binary64_84 *-un-lft-identity_binary64_78
60×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
12×distribute-lft-out_binary64_29
10×add-exp-log_binary64_116
pow1_binary64_139
add-cbrt-cube_binary64_114 add-log-exp_binary64_117 rem-log-exp_binary64_119
div-exp_binary64_129 pow1/3_binary64_160 div-inv_binary64_75 log-div_binary64_165 log-pow_binary64_167
Counts
4 → 136
Calls

8 calls:

8.0ms
(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))
7.0ms
(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))
1.0ms
(cbrt.f64 N)
1.0ms
(cbrt.f64 N)
0.0ms
(/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N))

series277.0ms (0.3%)

Counts
4 → 24
Calls

4 calls:

76.0ms
(cbrt.f64 N)
71.0ms
(cbrt.f64 N)
65.0ms
(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))
64.0ms
(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 N)))
Compiler

Compiled 752 to 654 computations (13% saved)

simplify103.0ms (0.1%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049563462
149563462

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(log.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (sqrt.f64 (cbrt.f64 N))))
0.0b
(sqrt.f64 (+.f64 N 1))
0.0b
(sqrt.f64 (+.f64 N 1))
0.0b
(log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N))))
0.3b
(/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N)))
0.6b
(cbrt.f64 N)
0.6b
(cbrt.f64 N)
4.2b
(+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N)))) (log.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (sqrt.f64 (cbrt.f64 N)))))

rewrite204.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
834×times-frac_binary64_84
709×sqrt-prod_binary64_94
544×*-un-lft-identity_binary64_78
443×log-prod_binary64_164
418×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 associate-+r+_binary64_10
144×cbrt-prod_binary64_109
65×distribute-lft-out_binary64_29
25×associate-+l+_binary64_11
12×div-inv_binary64_75
pow1_binary64_139
associate-/l*_binary64_23
add-cbrt-cube_binary64_114 add-exp-log_binary64_116
add-log-exp_binary64_117 log-pow_binary64_167
associate-/r*_binary64_22
flip-+_binary64_52 pow1/3_binary64_160 sqrt-div_binary64_95 log-div_binary64_165 associate-/l/_binary64_25 flip3-+_binary64_81
+-commutative_binary64_8 associate-+l-_binary64_13 associate-+r-_binary64_12 cbrt-undiv_binary64_112 div-exp_binary64_129 frac-2neg_binary64_89 clear-num_binary64_77 sum-log_binary64_169
Counts
4 → 527
Calls

8 calls:

74.0ms
(+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N)))) (log.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (sqrt.f64 (cbrt.f64 N)))))
6.0ms
(/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N)))
1.0ms
(cbrt.f64 N)
1.0ms
(cbrt.f64 N)
0.0ms
(log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N))))

series332.0ms (0.3%)

Counts
4 → 18
Calls

4 calls:

114.0ms
(+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N)))) (log.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (sqrt.f64 (cbrt.f64 N)))))
84.0ms
(cbrt.f64 N)
82.0ms
(cbrt.f64 N)
51.0ms
(/.f64 (sqrt.f64 (+.f64 N 1)) (fabs.f64 (cbrt.f64 N)))
Compiler

Compiled 785 to 665 computations (15.3% saved)

simplify235.0ms (0.2%)

Algorithm
egg-herbie
Counts
545 → 545
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0508219313

prune34.2s (33%)

Pruning

749 alts after pruning (736 fresh and 13 done)

PrunedKeptTotal
New617310927
Fresh16426442
Picked000
Done01313
Total6337491382
Error
0.0b
Counts
1382 → 749
Compiler

Compiled 14002 to 8462 computations (39.6% saved)

simplify791.0ms (0.8%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0502347109

regimes6.6s (6.4%)

Compiler

Compiled 53675 to 40485 computations (24.6% saved)

bsearch52.0ms (0%)

Compiler

Compiled 7 to 6 computations (14.3% saved)

regimes1.0s (1%)

Compiler

Compiled 7598 to 5969 computations (21.4% saved)

bsearch9.0ms (0%)

Compiler

Compiled 7 to 6 computations (14.3% saved)

regimes52.0ms (0%)

Compiler

Compiled 167 to 148 computations (11.4% saved)

bsearch19.0ms (0%)

Steps
ItersRangePoint
10
169.11543035470882
15665336860218.78
166837.4406959138
Compiler

Compiled 1 to 1 computations (0% saved)

regimes46.0ms (0%)

Compiler

Compiled 149 to 131 computations (12.1% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.0195769410811402
98.34028342914021
0.8974791688528108
Compiler

Compiled 1 to 1 computations (0% saved)

regimes44.0ms (0%)

Compiler

Compiled 135 to 119 computations (11.9% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.0195769410811402
98.34028342914021
0.6815557620276427
Compiler

Compiled 1 to 1 computations (0% saved)

regimes38.0ms (0%)

Compiler

Compiled 125 to 108 computations (13.6% saved)

bsearch13.0ms (0%)

Steps
ItersRangePoint
8
0.0195769410811402
98.34028342914021
0.8974791688528108
Compiler

Compiled 1 to 1 computations (0% saved)

regimes23.0ms (0%)

Compiler

Compiled 43 to 41 computations (4.7% saved)

bsearch12.0ms (0%)

Steps
ItersRangePoint
8
0.0195769410811402
98.34028342914021
0.9934451274417744
Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0%)

Accuracy

Total 0.5b remaining (97.8%)

Threshold costs 0.5b (97.8%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch8.0ms (0%)

Compiler

Compiled 136 to 105 computations (22.8% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
081204
181204

end0.0ms (0%)

sample29.4s (28.3%)

Algorithm
intervals
Results
447.0ms2031×body1024valid
234.0ms4204×body128valid
153.0ms1042×body512valid
74.0ms210×body2048valid
44.0ms513×body256valid
Compiler

Compiled 27195 to 20514 computations (24.6% saved)

Pareto

0.8931642525015486

Profiling

Loading profile data...