Details

Time bar (total: 51.2s)

analyze2.0ms (0%)

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 (0.1%)

Algorithm
intervals
Results
15.0ms70×body1024valid
8.0ms141×body128valid
3.0ms21×body512valid
3.0msbody2048valid
1.0ms17×body256valid
Compiler

Compiled 18 to 18 computations (0% saved)

simplify104.0ms (0.2%)

Algorithm
egg-herbie
Counts
3 → 3
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
07113
17113

prune2.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New033
Fresh033
Picked000
Done000
Total066
Error
28.1b
Counts
6 → 3
Compiler

Compiled 9 to 8 computations (11.1% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

3.3b
(log.f64 (+.f64 N 1))
2.1b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.1b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.3b
(log.f64 (+.f64 N 1))

rewrite14.0ms (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:

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

series88.0ms (0.2%)

Counts
2 → 21
Calls

2 calls:

58.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
30.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 296 to 255 computations (13.9% saved)

simplify86.0ms (0.2%)

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
04924853
14924853

prune260.0ms (0.5%)

Pruning

40 alts after pruning (39 fresh and 1 done)

PrunedKeptTotal
New283765
Fresh022
Picked000
Done011
Total284068
Error
0.0b
Counts
68 → 40
Compiler

Compiled 1088 to 766 computations (29.6% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

2.5b
(log.f64 (/.f64 (+.f64 N 1) N))
0.0b
(/.f64 (+.f64 N 1) N)
0.0b
(/.f64 (+.f64 N 1) N)
2.5b
(log.f64 (/.f64 (+.f64 N 1) N))

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
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:

6.0ms
(/.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))

series82.0ms (0.2%)

Counts
2 → 18
Calls

2 calls:

46.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
36.0ms
(/.f64 (+.f64 N 1) N)
Compiler

Compiled 198 to 182 computations (8.1% saved)

simplify65.0ms (0.1%)

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (48.0ms)

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

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

3.3b
(log.f64 (+.f64 N 1))
2.1b
(+.f64 (log.f64 (+.f64 N 1)) (neg.f64 (log.f64 N)))
2.1b
(+.f64 (log.f64 (+.f64 N 1)) (neg.f64 (log.f64 N)))
3.3b
(log.f64 (+.f64 N 1))

rewrite16.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity_binary64_78
11×log-prod_binary64_164
distribute-lft-out_binary64_29 pow1_binary64_139
log-pow_binary64_167
add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
associate-+l+_binary64_11 log-div_binary64_165 distribute-rgt-neg-in_binary64_36
add-log-exp_binary64_117 distribute-neg-in_binary64_39 flip-+_binary64_52 associate-+r+_binary64_10 add-exp-log_binary64_116 flip3-+_binary64_81
add-cbrt-cube_binary64_114 associate-+l-_binary64_13 sum-log_binary64_169
+-commutative_binary64_8 associate-+r-_binary64_12 rem-log-exp_binary64_119 neg-sub0_binary64_73 unsub-neg_binary64_72 neg-log_binary64_171
Counts
2 → 44
Calls

4 calls:

9.0ms
(+.f64 (log.f64 (+.f64 N 1)) (neg.f64 (log.f64 N)))
4.0ms
(log.f64 (+.f64 N 1))
0.0ms
(+.f64 (log.f64 (+.f64 N 1)) (neg.f64 (log.f64 N)))
0.0ms
(log.f64 (+.f64 N 1))

series91.0ms (0.2%)

Counts
2 → 21
Calls

2 calls:

59.0ms
(+.f64 (log.f64 (+.f64 N 1)) (neg.f64 (log.f64 N)))
31.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 306 to 265 computations (13.4% saved)

simplify64.0ms (0.1%)

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
04919833
14919833

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

24.4b
(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
3.3b
(log.f64 (+.f64 N 1))
0.8b
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
0.0b
(log.f64 (log.f64 (+.f64 N 1)))
0.0b
(log.f64 (log.f64 (+.f64 N 1)))
0.8b
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
3.3b
(log.f64 (+.f64 N 1))
24.4b
(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))

rewrite19.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×log-prod_binary64_164
15×*-un-lft-identity_binary64_78
14×add-sqr-sqrt_binary64_100
11×pow1_binary64_139
10×add-cube-cbrt_binary64_113
log-pow_binary64_167
add-exp-log_binary64_116
add-log-exp_binary64_117 exp-sum_binary64_124
add-cbrt-cube_binary64_114 exp-prod_binary64_130 cancel-sign-sub-inv_binary64_44
associate--r+_binary64_14
distribute-lft-out--_binary64_30 rem-log-exp_binary64_119 log-div_binary64_165 difference-of-squares_binary64_47
flip-+_binary64_52 flip3--_binary64_82 diff-log_binary64_170 rem-exp-log_binary64_118 flip--_binary64_53 distribute-lft-out_binary64_29 sub-neg_binary64_71 flip3-+_binary64_81
Counts
4 → 66
Calls

8 calls:

7.0ms
(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
3.0ms
(log.f64 (+.f64 N 1))
2.0ms
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
1.0ms
(log.f64 (log.f64 (+.f64 N 1)))
0.0ms
(log.f64 (log.f64 (+.f64 N 1)))

series258.0ms (0.5%)

Counts
4 → 36
Calls

4 calls:

92.0ms
(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
72.0ms
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
63.0ms
(log.f64 (log.f64 (+.f64 N 1)))
30.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 964 to 780 computations (19.1% saved)

simplify68.0ms (0.1%)

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
048721352
148721352

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
0.3b
(cbrt.f64 (+.f64 N 1))
0.3b
(cbrt.f64 (+.f64 N 1))
0.1b
(+.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 2) (log.f64 (cbrt.f64 (+.f64 N 1))))
0.3b
(cbrt.f64 (+.f64 N 1))
3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
8.7b
(-.f64 (+.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))

rewrite31.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64_78
17×log-prod_binary64_164
13×add-sqr-sqrt_binary64_100
12×cbrt-prod_binary64_109
11×add-cube-cbrt_binary64_113
cbrt-div_binary64_110 pow1_binary64_139
add-log-exp_binary64_117 add-exp-log_binary64_116 log-div_binary64_165 log-pow_binary64_167
add-cbrt-cube_binary64_114 flip-+_binary64_52 cancel-sign-sub-inv_binary64_44 flip3-+_binary64_81
pow1/3_binary64_160 associate--r+_binary64_14 distribute-lft-out_binary64_29
associate-+r-_binary64_12 distribute-lft-out--_binary64_30 diff-log_binary64_170 rem-log-exp_binary64_119 associate--l-_binary64_16
flip3--_binary64_82 associate--l+_binary64_15 flip--_binary64_53 difference-of-squares_binary64_47 sub-neg_binary64_71 sum-log_binary64_169
Counts
4 → 77
Calls

8 calls:

13.0ms
(-.f64 (+.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))
4.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
4.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
3.0ms
(cbrt.f64 (+.f64 N 1))
0.0ms
(+.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 2) (log.f64 (cbrt.f64 (+.f64 N 1))))

series222.0ms (0.4%)

Counts
4 → 36
Calls

4 calls:

65.0ms
(-.f64 (+.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))
57.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
53.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
47.0ms
(cbrt.f64 (+.f64 N 1))
Compiler

Compiled 933 to 818 computations (12.3% saved)

simplify64.0ms (0.1%)

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
048901564
148901564

prune3.7s (7.3%)

Pruning

169 alts after pruning (164 fresh and 5 done)

PrunedKeptTotal
New225133358
Fresh33134
Picked000
Done156
Total229169398
Error
0.0b
Counts
398 → 169
Compiler

Compiled 6658 to 4890 computations (26.6% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

2.5b
(log.f64 (/.f64 (-.f64 -1 N) (neg.f64 N)))
0.0b
(/.f64 (-.f64 -1 N) (neg.f64 N))
0.0b
(/.f64 (-.f64 -1 N) (neg.f64 N))
2.5b
(log.f64 (/.f64 (-.f64 -1 N) (neg.f64 N)))

rewrite32.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
100×times-frac_binary64_84
99×add-sqr-sqrt_binary64_100 *-un-lft-identity_binary64_78
57×add-cube-cbrt_binary64_113
54×log-prod_binary64_164
33×distribute-lft-neg-in_binary64_35 distribute-rgt-neg-in_binary64_36
21×distribute-lft-out--_binary64_30 difference-of-squares_binary64_47
11×neg-mul-1_binary64_74
10×associate-/r*_binary64_22
add-exp-log_binary64_116
associate-/l*_binary64_23
add-cbrt-cube_binary64_114
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 flip3--_binary64_82 frac-2neg_binary64_89 flip--_binary64_53 log-div_binary64_165 clear-num_binary64_77 log-pow_binary64_167 div-sub_binary64_83
Counts
2 → 145
Calls

4 calls:

8.0ms
(/.f64 (-.f64 -1 N) (neg.f64 N))
7.0ms
(log.f64 (/.f64 (-.f64 -1 N) (neg.f64 N)))
0.0ms
(/.f64 (-.f64 -1 N) (neg.f64 N))
0.0ms
(log.f64 (/.f64 (-.f64 -1 N) (neg.f64 N)))

series76.0ms (0.1%)

Counts
2 → 18
Calls

2 calls:

45.0ms
(log.f64 (/.f64 (-.f64 -1 N) (neg.f64 N)))
31.0ms
(/.f64 (-.f64 -1 N) (neg.f64 N))
Compiler

Compiled 198 to 182 computations (8.1% saved)

simplify83.0ms (0.2%)

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050553019

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b
(/.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)))
0.5b
(/.f64 1/2 (*.f64 N N))

rewrite21.0ms (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:

13.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
5.0ms
(/.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))

series66.0ms (0.1%)

Counts
2 → 9
Calls

2 calls:

41.0ms
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
25.0ms
(/.f64 1/2 (*.f64 N N))
Compiler

Compiled 131 to 119 computations (9.2% saved)

simplify95.0ms (0.2%)

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
04864753
14864753

localize12.0ms (0%)

Local error

Found 6 expressions with local error:

15.8b
(log.f64 (-.f64 (*.f64 N N) 1))
2.4b
(+.f64 (-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1))) (neg.f64 (log.f64 N)))
0.0b
(-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1)))
0.0b
(-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1)))
2.4b
(+.f64 (-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1))) (neg.f64 (log.f64 N)))
15.8b
(log.f64 (-.f64 (*.f64 N N) 1))

rewrite44.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity_binary64_78
28×log-prod_binary64_164
27×pow1_binary64_139
24×log-pow_binary64_167
19×add-sqr-sqrt_binary64_100
17×distribute-lft-out--_binary64_30
15×distribute-lft-out_binary64_29
13×associate-+l+_binary64_11
12×associate--l+_binary64_15
10×add-cube-cbrt_binary64_113 distribute-rgt-neg-in_binary64_36
difference-of-squares_binary64_47
log-div_binary64_165 cancel-sign-sub-inv_binary64_44
add-log-exp_binary64_117 associate--r+_binary64_14
flip3--_binary64_82 flip--_binary64_53
associate--r-_binary64_17 add-exp-log_binary64_116 difference-of-sqr-1_binary64_48 sum-log_binary64_169
add-cbrt-cube_binary64_114 distribute-neg-in_binary64_39 diff-log_binary64_170 associate-+r+_binary64_10
associate--l-_binary64_16 sub-neg_binary64_71 neg-log_binary64_171
+-commutative_binary64_8 associate-+l-_binary64_13 associate-+r-_binary64_12 flip-+_binary64_52 rem-log-exp_binary64_119 neg-sub0_binary64_73 unsub-neg_binary64_72 flip3-+_binary64_81
Counts
3 → 102
Calls

6 calls:

17.0ms
(+.f64 (-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1))) (neg.f64 (log.f64 N)))
12.0ms
(-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1)))
5.0ms
(log.f64 (-.f64 (*.f64 N N) 1))
0.0ms
(-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1)))
0.0ms
(+.f64 (-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1))) (neg.f64 (log.f64 N)))

series144.0ms (0.3%)

Counts
3 → 24
Calls

3 calls:

59.0ms
(+.f64 (-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1))) (neg.f64 (log.f64 N)))
44.0ms
(-.f64 (log.f64 (-.f64 (*.f64 N N) 1)) (log.f64 (-.f64 N 1)))
41.0ms
(log.f64 (-.f64 (*.f64 N N) 1))
Compiler

Compiled 428 to 372 computations (13.1% saved)

simplify160.0ms (0.3%)

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (133.0ms)

IterNodesCost
048711647
148711647

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

2.1b
(+.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N))) (neg.f64 (log.f64 (sqrt.f64 N))))
0.0b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N)))
0.0b
(log.f64 (sqrt.f64 N))
0.0b
(log.f64 (sqrt.f64 N))
0.0b
(log.f64 (sqrt.f64 N))
0.0b
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N)))
2.1b
(+.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N))) (neg.f64 (log.f64 (sqrt.f64 N))))
3.3b
(log.f64 (+.f64 N 1))

rewrite43.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity_binary64_78
32×pow1_binary64_139
31×log-pow_binary64_167
30×log-prod_binary64_164
18×distribute-lft-out_binary64_29
17×add-sqr-sqrt_binary64_100
16×distribute-lft-out--_binary64_30
15×add-cube-cbrt_binary64_113
12×cancel-sign-sub-inv_binary64_44
11×associate-+l+_binary64_11
10×distribute-rgt-neg-in_binary64_36
sqrt-prod_binary64_94
add-log-exp_binary64_117 associate--l+_binary64_15
distribute-neg-in_binary64_39 associate-+r+_binary64_10 associate--r+_binary64_14 add-exp-log_binary64_116
add-cbrt-cube_binary64_114 log-div_binary64_165 sum-log_binary64_169
sqrt-pow1_binary64_96 flip-+_binary64_52 diff-log_binary64_170 pow1/2_binary64_158 flip3-+_binary64_81
rem-log-exp_binary64_119 associate--l-_binary64_16 sub-neg_binary64_71 neg-log_binary64_171
+-commutative_binary64_8 associate-+l-_binary64_13 associate-+r-_binary64_12 flip3--_binary64_82 flip--_binary64_53 neg-sub0_binary64_73 difference-of-squares_binary64_47 unsub-neg_binary64_72
Counts
4 → 115
Calls

8 calls:

19.0ms
(+.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N))) (neg.f64 (log.f64 (sqrt.f64 N))))
9.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N)))
4.0ms
(log.f64 (+.f64 N 1))
2.0ms
(log.f64 (sqrt.f64 N))
0.0ms
(log.f64 (sqrt.f64 N))

series113.0ms (0.2%)

Counts
4 → 18
Calls

4 calls:

37.0ms
(+.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N))) (neg.f64 (log.f64 (sqrt.f64 N))))
32.0ms
(log.f64 (+.f64 N 1))
27.0ms
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 (sqrt.f64 N)))
16.0ms
(log.f64 (sqrt.f64 N))
Compiler

Compiled 502 to 411 computations (18.1% saved)

simplify125.0ms (0.2%)

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (103.0ms)

IterNodesCost
048631550
148631550

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3))
0.3b
(cbrt.f64 (+.f64 N 1))
0.3b
(cbrt.f64 (+.f64 N 1))
0.1b
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1))))
0.4b
(pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)
3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
8.7b
(-.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))

rewrite34.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64_78
17×log-prod_binary64_164
15×add-sqr-sqrt_binary64_100
13×add-cube-cbrt_binary64_113
11×pow1_binary64_139
10×log-pow_binary64_167
cbrt-prod_binary64_109
add-exp-log_binary64_116
cbrt-div_binary64_110 add-log-exp_binary64_117 log-div_binary64_165
add-cbrt-cube_binary64_114 unpow-prod-down_binary64_157 cube-prod_binary64_106
pow1/3_binary64_160 cancel-sign-sub-inv_binary64_44
flip-+_binary64_52 associate--r+_binary64_14 pow-unpow_binary64_155 flip3-+_binary64_81
associate-+r-_binary64_12 distribute-lft-out--_binary64_30 diff-log_binary64_170 rem-log-exp_binary64_119 distribute-lft-out_binary64_29 associate--l-_binary64_16
rem-cube-cbrt_binary64_101 cube-mult_binary64_108 pow-exp_binary64_146 pow-to-exp_binary64_147 flip3--_binary64_82 sqr-pow_binary64_50 associate--l+_binary64_15 pow-pow_binary64_150 flip--_binary64_53 difference-of-squares_binary64_47 unpow3_binary64_144 sub-neg_binary64_71 sum-log_binary64_169
Counts
4 → 90
Calls

8 calls:

13.0ms
(-.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))
4.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
4.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
4.0ms
(pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)
0.0ms
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1))))

series287.0ms (0.6%)

Counts
4 → 36
Calls

4 calls:

98.0ms
(pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)
65.0ms
(-.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))
63.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
61.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
Compiler

Compiled 1107 to 975 computations (11.9% saved)

simplify90.0ms (0.2%)

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
048891872
148891872

prune10.7s (20.9%)

Pruning

328 alts after pruning (318 fresh and 10 done)

PrunedKeptTotal
New426179605
Fresh20139159
Picked000
Done01010
Total446328774
Error
0.0b
Counts
774 → 328
Compiler

Compiled 12921 to 9235 computations (28.5% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

2.9b
(exp.f64 (log.f64 (/.f64 (+.f64 N 1) N)))
2.5b
(log.f64 (exp.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
2.5b
(log.f64 (/.f64 (+.f64 N 1) N))
0.0b
(/.f64 (+.f64 N 1) N)
0.0b
(/.f64 (+.f64 N 1) N)
2.5b
(log.f64 (exp.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
2.5b
(log.f64 (/.f64 (+.f64 N 1) N))
2.9b
(exp.f64 (log.f64 (/.f64 (+.f64 N 1) N)))

rewrite34.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
67×log-prod_binary64_164
66×*-un-lft-identity_binary64_78
48×times-frac_binary64_84
40×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
32×exp-sum_binary64_124
13×distribute-lft-out_binary64_29
add-exp-log_binary64_116
exp-prod_binary64_130 log-pow_binary64_167 pow1_binary64_139
add-cbrt-cube_binary64_114
add-log-exp_binary64_117 div-inv_binary64_75 associate-/l*_binary64_23 log-div_binary64_165
rem-log-exp_binary64_119 associate-/r*_binary64_22
div-exp_binary64_129 exp-diff_binary64_126 associate-/l/_binary64_25
cbrt-undiv_binary64_112 flip-+_binary64_52 rem-exp-log_binary64_118 frac-2neg_binary64_89 clear-num_binary64_77 flip3-+_binary64_81
Counts
4 → 122
Calls

8 calls:

7.0ms
(log.f64 (exp.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
6.0ms
(exp.f64 (log.f64 (/.f64 (+.f64 N 1) N)))
6.0ms
(/.f64 (+.f64 N 1) N)
5.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
0.0ms
(/.f64 (+.f64 N 1) N)

series275.0ms (0.5%)

Counts
4 → 36
Calls

4 calls:

120.0ms
(exp.f64 (log.f64 (/.f64 (+.f64 N 1) N)))
72.0ms
(log.f64 (exp.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
48.0ms
(log.f64 (/.f64 (+.f64 N 1) N))
34.0ms
(/.f64 (+.f64 N 1) N)
Compiler

Compiled 461 to 419 computations (9.1% saved)

simplify121.0ms (0.2%)

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
048852127
148852127

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(/.f64 -1/2 (*.f64 N N))
0.5b
(/.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))

series26.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

26.0ms
(/.f64 -1/2 (*.f64 N N))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify89.0ms (0.2%)

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
04675212
14675212

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

24.4b
(+.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (neg.f64 (log.f64 N)))
3.3b
(log.f64 (+.f64 N 1))
0.8b
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
0.0b
(log.f64 (log.f64 (+.f64 N 1)))
0.0b
(log.f64 (log.f64 (+.f64 N 1)))
0.8b
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
3.3b
(log.f64 (+.f64 N 1))
24.4b
(+.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (neg.f64 (log.f64 N)))

rewrite21.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity_binary64_78
15×log-prod_binary64_164
10×pow1_binary64_139
add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113
add-log-exp_binary64_117
add-exp-log_binary64_116 log-pow_binary64_167
add-cbrt-cube_binary64_114 exp-sum_binary64_124 exp-prod_binary64_130 distribute-lft-out_binary64_29
distribute-neg-in_binary64_39 associate-+r+_binary64_10
flip-+_binary64_52 rem-log-exp_binary64_119 log-div_binary64_165 distribute-rgt-neg-in_binary64_36 sum-log_binary64_169 flip3-+_binary64_81
+-commutative_binary64_8 associate-+r-_binary64_12 rem-exp-log_binary64_118 neg-sub0_binary64_73 unsub-neg_binary64_72 neg-log_binary64_171
Counts
4 → 64
Calls

8 calls:

9.0ms
(+.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (neg.f64 (log.f64 N)))
3.0ms
(log.f64 (+.f64 N 1))
2.0ms
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
1.0ms
(log.f64 (log.f64 (+.f64 N 1)))
0.0ms
(log.f64 (log.f64 (+.f64 N 1)))

series248.0ms (0.5%)

Counts
4 → 36
Calls

4 calls:

90.0ms
(+.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (neg.f64 (log.f64 N)))
70.0ms
(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
58.0ms
(log.f64 (log.f64 (+.f64 N 1)))
30.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 994 to 810 computations (18.5% saved)

simplify78.0ms (0.2%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
057831314

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b
(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)))
0.4b
(pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)
0.3b
(cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3))
0.0b
(log.f64 (log.f64 (+.f64 N 1)))
0.4b
(pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)
0.8b
(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)))
3.3b
(log.f64 (+.f64 N 1))
24.4b
(-.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3))) (log.f64 N))

rewrite27.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_78
17×exp-prod_binary64_130
16×add-sqr-sqrt_binary64_100
14×add-cube-cbrt_binary64_113 cbrt-prod_binary64_109
12×pow1_binary64_139
unpow-prod-down_binary64_157 cube-prod_binary64_106
log-prod_binary64_164 log-pow_binary64_167
add-log-exp_binary64_117 add-exp-log_binary64_116
add-cbrt-cube_binary64_114
cancel-sign-sub-inv_binary64_44
associate--r+_binary64_14 pow-unpow_binary64_155
cube-mult_binary64_108 distribute-lft-out--_binary64_30 sqr-pow_binary64_50 log-div_binary64_165 unpow3_binary64_144
rem-cube-cbrt_binary64_101 pow-exp_binary64_146 pow-to-exp_binary64_147 flip-+_binary64_52 flip3--_binary64_82 diff-log_binary64_170 rem-exp-log_binary64_118 pow-pow_binary64_150 flip--_binary64_53 rem-log-exp_binary64_119 difference-of-squares_binary64_47 distribute-lft-out_binary64_29 sub-neg_binary64_71 flip3-+_binary64_81
Counts
4 → 86
Calls

8 calls:

9.0ms
(-.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3))) (log.f64 N))
5.0ms
(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)))
3.0ms
(log.f64 (+.f64 N 1))
2.0ms
(pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)
0.0ms
(log.f64 (log.f64 (+.f64 N 1)))

series421.0ms (0.8%)

Counts
4 → 36
Calls

4 calls:

225.0ms
(pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)
89.0ms
(-.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3))) (log.f64 N))
69.0ms
(exp.f64 (cbrt.f64 (pow.f64 (log.f64 (log.f64 (+.f64 N 1))) 3)))
38.0ms
(log.f64 (+.f64 N 1))
Compiler

Compiled 1263 to 1032 computations (18.3% saved)

simplify76.0ms (0.1%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
048881903
148881903

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3))
0.3b
(cbrt.f64 (+.f64 N 1))
0.3b
(cbrt.f64 (+.f64 N 1))
0.1b
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1))))
0.4b
(pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)
3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
3.3b
(log.f64 (cbrt.f64 (+.f64 N 1)))
8.7b
(-.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))

rewrite33.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64_78
17×log-prod_binary64_164
15×add-sqr-sqrt_binary64_100
13×add-cube-cbrt_binary64_113
11×pow1_binary64_139
10×log-pow_binary64_167
cbrt-prod_binary64_109
add-exp-log_binary64_116
cbrt-div_binary64_110 add-log-exp_binary64_117 log-div_binary64_165
add-cbrt-cube_binary64_114 unpow-prod-down_binary64_157 cube-prod_binary64_106
pow1/3_binary64_160 cancel-sign-sub-inv_binary64_44
flip-+_binary64_52 associate--r+_binary64_14 pow-unpow_binary64_155 flip3-+_binary64_81
associate-+r-_binary64_12 distribute-lft-out--_binary64_30 diff-log_binary64_170 rem-log-exp_binary64_119 distribute-lft-out_binary64_29 associate--l-_binary64_16
rem-cube-cbrt_binary64_101 cube-mult_binary64_108 pow-exp_binary64_146 pow-to-exp_binary64_147 flip3--_binary64_82 sqr-pow_binary64_50 associate--l+_binary64_15 pow-pow_binary64_150 flip--_binary64_53 difference-of-squares_binary64_47 unpow3_binary64_144 sub-neg_binary64_71 sum-log_binary64_169
Counts
4 → 90
Calls

8 calls:

13.0ms
(-.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))
4.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
4.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
4.0ms
(pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)
0.0ms
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1))))

series289.0ms (0.6%)

Counts
4 → 36
Calls

4 calls:

104.0ms
(pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)
69.0ms
(-.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) 3)) 2) (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 N))
59.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
56.0ms
(log.f64 (cbrt.f64 (+.f64 N 1)))
Compiler

Compiled 1187 to 1055 computations (11.1% saved)

simplify99.0ms (0.2%)

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
048891872
148891872

prune17.1s (33.4%)

Pruning

490 alts after pruning (476 fresh and 14 done)

PrunedKeptTotal
New333197530
Fresh34279313
Picked000
Done11415
Total368490858
Error
0.0b
Counts
858 → 490
Compiler

Compiled 6450 to 4514 computations (30% saved)

simplify359.0ms (0.7%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
0503223487

regimes1.8s (3.5%)

Compiler

Compiled 10011 to 7961 computations (20.5% saved)

bsearch34.0ms (0.1%)

Steps
ItersRangePoint
8
40.575275526118034
105906.85642316272
1511.9843372896694
Compiler

Compiled 1 to 1 computations (0% saved)

regimes141.0ms (0.3%)

Compiler

Compiled 715 to 562 computations (21.4% saved)

bsearch17.0ms (0%)

Steps
ItersRangePoint
8
40.575275526118034
105906.85642316272
8944.961044310863
Compiler

Compiled 1 to 1 computations (0% saved)

regimes70.0ms (0.1%)

Compiler

Compiled 302 to 241 computations (20.2% saved)

bsearch16.0ms (0%)

Steps
ItersRangePoint
9
105906.85642316272
91642270830.06389
204410.2502577827
Compiler

Compiled 1 to 1 computations (0% saved)

regimes40.0ms (0.1%)

Compiler

Compiled 122 to 106 computations (13.1% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.902128626469268
Compiler

Compiled 1 to 1 computations (0% saved)

regimes37.0ms (0.1%)

Compiler

Compiled 114 to 99 computations (13.2% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.6844505345468515
Compiler

Compiled 1 to 1 computations (0% saved)

regimes35.0ms (0.1%)

Compiler

Compiled 107 to 92 computations (14% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.902128626469268
Compiler

Compiled 1 to 1 computations (0% saved)

regimes22.0ms (0%)

Compiler

Compiled 44 to 40 computations (9.1% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.9891998632382345
Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0%)

Accuracy

Total 0.0b remaining (46.7%)

Threshold costs 0.0b (46.7%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch8.0ms (0%)

Compiler

Compiled 132 to 103 computations (22% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
090193
190193

end0.0ms (0%)

sample12.0s (23.5%)

Algorithm
intervals
Results
448.0ms1967×body1024valid
247.0ms4304×body128valid
137.0ms967×body512valid
89.0ms244×body2048valid
45.0ms518×body256valid
Compiler

Compiled 10281 to 8173 computations (20.5% saved)

Pareto

0.733163442055186

Profiling

Loading profile data...