Details

Time bar (total: 36.2s)

analyze1.4s (3.9%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0524238
022
122
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%50%22%7
28.1%46.8%25.1%8
29.7%41.4%29%9
29.7%39.4%30.9%10
31.1%35.8%33.1%11
31.1%34.4%34.5%12
31.5%32.9%35.6%13
31.5%32.1%36.4%14
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample247.0ms (0.7%)

Algorithm
intervals
Results
53.0ms82×body1024valid
45.0ms47×body1024nan
38.0ms51×body2048valid
27.0ms50×body512valid
19.0ms89×body128overflowed
16.0ms30×body512nan
6.0ms56×body128valid
6.0msbody1024invalid
5.0ms17×body256valid
3.0msbody512invalid
2.0ms28×body128nan
1.0ms10×body128invalid
1.0msbody256invalid
1.0msbody256nan
1.0msbody2048nan
Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify74.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0483119
1483119

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
33.5b
Counts
2 → 1
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(pow.f64 x (/.f64 1 n))
2.3b
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite123.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
33.5b
Rules
24×add-sqr-sqrt_binary64_100
19×*-un-lft-identity_binary64_78
16×unpow-prod-down_binary64_157
13×pow-unpow_binary64_155
12×add-cube-cbrt_binary64_113
difference-of-squares_binary64_47 times-frac_binary64_84
sqr-pow_binary64_50
cancel-sign-sub-inv_binary64_44
add-log-exp_binary64_117
pow1_binary64_139 add-exp-log_binary64_116 distribute-lft-out--_binary64_30
add-cbrt-cube_binary64_114
diff-log_binary64_170 flip3--_binary64_82 sub-neg_binary64_71 flip--_binary64_53 distribute-lft-out_binary64_29 div-inv_binary64_75 pow-pow_binary64_150 pow-to-exp_binary64_147 pow-exp_binary64_146
Counts
2 → 57
Calls

2 calls:

10.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
3.0ms
(pow.f64 x (/.f64 1 n))
Compiler

Compiled 1342 to 963 computations (28.2% saved)

series563.0ms (1.6%)

Error
1.1b
Counts
2 → 28
Calls

2 calls:

350.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
138.0ms
(pow.f64 x (/.f64 1 n))
Compiler

Compiled 2150 to 1648 computations (23.3% saved)

simplify80.0ms (0.2%)

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049552087
149552087

prune155.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New80585
Fresh000
Picked101
Done000
Total81586
Error
1.0b
Counts
86 → 5
Compiler

Compiled 2185 to 1466 computations (32.9% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b
(log.f64 (+.f64 1 x))
1.4b
(log.f64 (+.f64 1 x))
1.7b
(+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (-.f64 (*.f64 (/.f64 1/2 n) (-.f64 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) n) (/.f64 (pow.f64 (log.f64 x) 2) n))) (/.f64 (log.f64 x) n)))
3.0b
(-.f64 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) n) (/.f64 (pow.f64 (log.f64 x) 2) n))

rewrite907.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
1.0b
Rules
163×times-frac_binary64_84
142×add-sqr-sqrt_binary64_100
109×cancel-sign-sub-inv_binary64_44
98×*-un-lft-identity_binary64_78
81×associate-+r+_binary64_10
72×add-cube-cbrt_binary64_113
70×unpow-prod-down_binary64_157
64×associate--l+_binary64_15
32×distribute-rgt-in_binary64_28 distribute-lft-in_binary64_27
30×pow1_binary64_139
26×log-pow_binary64_167
25×difference-of-squares_binary64_47
19×unpow2_binary64_143 sqr-pow_binary64_50
16×distribute-lft-out--_binary64_30
13×frac-add_binary64_86
12×frac-sub_binary64_87
11×add-log-exp_binary64_117
log-prod_binary64_164
add-exp-log_binary64_116 sub-div_binary64_85 div-inv_binary64_75 log-div_binary64_165
associate-*r/_binary64_20
add-cbrt-cube_binary64_114 flip3--_binary64_82 sub-neg_binary64_71 flip--_binary64_53 frac-times_binary64_88 flip3-+_binary64_81 flip-+_binary64_52
distribute-lft-out_binary64_29
diff-log_binary64_170 sum-log_binary64_169 associate-*l/_binary64_21 div-sub_binary64_83 associate-+l-_binary64_13 rem-log-exp_binary64_119
distribute-rgt-out--_binary64_32 associate-+r-_binary64_12 +-commutative_binary64_8
Counts
4 → 226
Calls

4 calls:

92.0ms
(+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (-.f64 (*.f64 (/.f64 1/2 n) (-.f64 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) n) (/.f64 (pow.f64 (log.f64 x) 2) n))) (/.f64 (log.f64 x) n)))
73.0ms
(-.f64 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) n) (/.f64 (pow.f64 (log.f64 x) 2) n))
6.0ms
(log.f64 (+.f64 1 x))
3.0ms
(log.f64 (+.f64 1 x))
Compiler

Compiled 10644 to 6530 computations (38.7% saved)

series1.2s (3.3%)

Error
0.7b
Counts
4 → 35
Calls

4 calls:

732.0ms
(+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (-.f64 (*.f64 (/.f64 1/2 n) (-.f64 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) n) (/.f64 (pow.f64 (log.f64 x) 2) n))) (/.f64 (log.f64 x) n)))
320.0ms
(-.f64 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) n) (/.f64 (pow.f64 (log.f64 x) 2) n))
44.0ms
(log.f64 (+.f64 1 x))
26.0ms
(log.f64 (+.f64 1 x))
Compiler

Compiled 3029 to 2230 computations (26.4% saved)

simplify134.0ms (0.4%)

Algorithm
egg-herbie
Counts
261 → 261
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050828709

prune850.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2547261
Fresh134
Picked101
Done000
Total25610266
Error
0.6b
Counts
266 → 10
Compiler

Compiled 11471 to 6864 computations (40.2% saved)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b
(+.f64 (*.f64 (log.f64 (+.f64 x 1)) (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n))) (-.f64 (*.f64 n (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)) (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n)))) (*.f64 (log.f64 x) (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)))))
3.3b
(-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2))
5.6b
(/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n))
6.5b
(*.f64 n (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)) (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n))))

rewrite4.2s (11.7%)

Algorithm
rewrite-expression-head
Error
0.6b
Rules
251×associate-*r/_binary64_20
158×frac-add_binary64_86
75×flip3-+_binary64_81 flip-+_binary64_52
63×frac-sub_binary64_87
41×add-exp-log_binary64_116 add-cbrt-cube_binary64_114 associate-*l/_binary64_21
30×frac-times_binary64_88
23×add-sqr-sqrt_binary64_100
20×unpow-prod-down_binary64_157
19×prod-exp_binary64_127 cbrt-unprod_binary64_111
16×difference-of-squares_binary64_47
14×pow1_binary64_139
13×*-un-lft-identity_binary64_78
12×sub-div_binary64_85
11×add-log-exp_binary64_117
10×cancel-sign-sub-inv_binary64_44
unpow2_binary64_143 sqr-pow_binary64_50
div-exp_binary64_129 cbrt-undiv_binary64_112
add-cube-cbrt_binary64_113
flip3--_binary64_82 flip--_binary64_53 log-pow_binary64_167 distribute-lft-out--_binary64_30
pow-prod-down_binary64_149 associate-*l*_binary64_19
associate-/l/_binary64_25 diff-log_binary64_170 sub-neg_binary64_71 sum-log_binary64_169 associate-+l+_binary64_11 associate-+r+_binary64_10
associate-*r*_binary64_18 *-commutative_binary64_9 frac-2neg_binary64_89 times-frac_binary64_84 clear-num_binary64_77 div-inv_binary64_75 associate-/l*_binary64_23 associate-/r*_binary64_22 associate-+r-_binary64_12 distribute-rgt-in_binary64_28 distribute-lft-in_binary64_27 +-commutative_binary64_8
Counts
4 → 195
Calls

4 calls:

147.0ms
(+.f64 (*.f64 (log.f64 (+.f64 x 1)) (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n))) (-.f64 (*.f64 n (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)) (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n)))) (*.f64 (log.f64 x) (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)))))
98.0ms
(*.f64 n (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)) (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n))))
32.0ms
(/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n))
21.0ms
(-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2))
Compiler

Compiled 36630 to 24227 computations (33.9% saved)

series3.6s (10.1%)

Error
0.6b
Counts
4 → 33
Calls

4 calls:

2.1s
(+.f64 (*.f64 (log.f64 (+.f64 x 1)) (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n))) (-.f64 (*.f64 n (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)) (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n)))) (*.f64 (log.f64 x) (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)))))
960.0ms
(*.f64 n (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) 2) n) (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) n)) (/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n))))
309.0ms
(/.f64 (*.f64 (-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2)) 1/2) (*.f64 n n))
107.0ms
(-.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (pow.f64 (log.f64 x) 2))
Compiler

Compiled 8198 to 5936 computations (27.6% saved)

simplify384.0ms (1.1%)

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0515032259

prune3.3s (9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2271228
Fresh099
Picked011
Done000
Total22711238
Error
0.6b
Counts
238 → 11
Compiler

Compiled 33477 to 21865 computations (34.7% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b
(/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))
3.3b
(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
6.0b
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
9.0b
(-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))

rewrite584.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0.6b
Rules
17×add-exp-log_binary64_116 *-un-lft-identity_binary64_78
15×add-log-exp_binary64_117
13×add-sqr-sqrt_binary64_100
11×pow1_binary64_139 add-cube-cbrt_binary64_113
add-cbrt-cube_binary64_114 associate-*r/_binary64_20 times-frac_binary64_84 associate-/l*_binary64_23
unpow-prod-down_binary64_157
cube-div_binary64_107 log-pow_binary64_167 log-prod_binary64_164
div-exp_binary64_129
frac-add_binary64_86 frac-sub_binary64_87 cancel-sign-sub-inv_binary64_44 associate--l+_binary64_15
sum-log_binary64_169 diff-log_binary64_170 flip3-+_binary64_81 flip-+_binary64_52 distribute-lft-out--_binary64_30
associate--l-_binary64_16 associate--r+_binary64_14 prod-exp_binary64_127
flip3--_binary64_82 sub-neg_binary64_71 flip--_binary64_53 log-div_binary64_165 pow-to-exp_binary64_147 pow-exp_binary64_146 cbrt-undiv_binary64_112 unpow2_binary64_143 sqr-pow_binary64_50
div-sub_binary64_83 associate-+r-_binary64_12 +-commutative_binary64_8 difference-of-squares_binary64_47 distribute-lft-out_binary64_29 cbrt-unprod_binary64_111 frac-2neg_binary64_89 clear-num_binary64_77 div-inv_binary64_75 associate-/r*_binary64_22
Counts
4 → 99
Calls

4 calls:

27.0ms
(-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
11.0ms
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
8.0ms
(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
8.0ms
(/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))
Compiler

Compiled 7173 to 4799 computations (33.1% saved)

series2.3s (6.3%)

Error
0.6b
Counts
4 → 52
Calls

4 calls:

1.2s
(-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
594.0ms
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
187.0ms
(/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))
100.0ms
(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
Compiler

Compiled 7210 to 5381 computations (25.4% saved)

simplify99.0ms (0.3%)

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050006052

prune664.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1474151
Fresh189
Picked101
Done011
Total14913162
Error
0.6b
Counts
162 → 13
Compiler

Compiled 9520 to 6170 computations (35.2% saved)

regimes2.2s (6.1%)

Accuracy

Total 6.8b remaining (97.1%)

Threshold costs 0b (0%)

Compiler

Compiled 23309 to 16684 computations (28.4% saved)

bsearch71.0ms (0.2%)

Steps
ItersRangePoint
8
8939932.848195631
6252137620.912037
9093778.054138303
Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07599
17599

end0.0ms (0%)

sample12.9s (35.7%)

Algorithm
intervals
Results
1.9s2720×body1024valid
1.4s1444×body1024nan
1.3s1732×body2048valid
610.0ms2636×body128overflowed
544.0ms1176×body512valid
424.0ms726×body512nan
224.0ms204×body1024invalid
216.0ms1816×body128valid
164.0ms556×body256valid
160.0ms242×body512invalid
107.0ms350×body256nan
66.0ms797×body128nan
54.0ms153×body256invalid
46.0ms291×body128invalid
4.0msbody2048nan
2.0msbody2048invalid
Compiler

Compiled 5771 to 4120 computations (28.6% saved)

Profiling

Loading profile data...