Details

Time bar (total: 42.5s)

analyze14.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%23.7%76.3%0
0%23.7%76.3%1
11.9%11.9%76.3%2
17.8%5.9%76.3%3
20.8%3%76.3%4
22.2%1.5%76.3%5
23%0.7%76.3%6
23.3%0.4%76.3%7
23.3%0.4%76.3%8
23.4%0.3%76.3%9
23.5%0.2%76.3%10
23.5%0.2%76.3%11
23.5%0.2%76.3%12
23.6%0.2%76.3%13
23.6%0.1%76.3%14
Compiler

Compiled 18 to 14 computations (22.2% saved)

sample79.0ms (0.2%)

Algorithm
1×intervals
Results
44.0ms137×body1024valid
11.0ms57×body512valid
8.0ms18×body2048valid
5.0ms41×body256valid
3.0ms256×pre128true
0.0ms3×body128valid
Compiler

Compiled 33 to 27 computations (18.2% saved)

simplify342.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (246.0ms)

IterNodesCost
0609423

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
63.0b
Counts
2 → 1
Compiler

Compiled 15 to 12 computations (20% saved)

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

6.1b
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n)))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 n (log.f64 n))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 n (log.f64 n))
6.1b
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n)))

rewrite39.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×log-prod_binary64_505
25×*-un-lft-identity_binary64_419
19×add-sqr-sqrt_binary64_441
15×add-cube-cbrt_binary64_454
14×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368
9×pow1_binary64_480
8×associate--l+_binary64_356 associate-*r*_binary64_359
7×associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
6×associate--r+_binary64_355
5×add-log-exp_binary64_458 distribute-lft-out_binary64_370
2×associate-*l/_binary64_362 pow-prod-down_binary64_490 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 log-pow_binary64_508 *-commutative_binary64_350
1×flip3-+_binary64_422 sub-neg_binary64_412 flip3--_binary64_423 flip-+_binary64_393 diff-log_binary64_511 flip--_binary64_394 cancel-sign-sub-inv_binary64_385
Counts
3 → 81
Calls

6 calls:

13.0ms
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n)))
9.0ms
(*.f64 n (log.f64 n))
9.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.0ms
(*.f64 n (log.f64 n))
0.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))

series155.0ms (0.4%)

Counts
3 → 11
Calls

3 calls:

77.0ms
(*.f64 n (log.f64 n))
48.0ms
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n)))
30.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
Compiler

Compiled 321 to 269 computations (16.2% saved)

simplify77.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049811480
149811480

prune415.0ms (1%)

Pruning

44 alts after pruning (43 fresh and 1 done)

PrunedKeptTotal
New494392
Fresh000
Picked000
Done011
Total494493
Error
0.0b
Counts
93 → 44
Compiler

Compiled 2342 to 1586 computations (32.3% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (+.f64 1 (log.f64 n)) 1)
0.0b
(+.f64 1 (log.f64 n))
0.0b
(+.f64 1 (log.f64 n))
0.0b
(-.f64 (+.f64 1 (log.f64 n)) 1)

rewrite14.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
15×*-un-lft-identity_binary64_419
8×add-sqr-sqrt_binary64_441
7×add-log-exp_binary64_458
4×add-cube-cbrt_binary64_454 distribute-lft-out_binary64_370 pow1_binary64_480
3×associate-+r+_binary64_351 log-prod_binary64_505 distribute-lft-out--_binary64_371 cancel-sign-sub-inv_binary64_385
2×difference-of-squares_binary64_388 sum-log_binary64_510 log-pow_binary64_508 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 diff-log_binary64_511
1×flip3-+_binary64_422 associate--l+_binary64_356 sub-neg_binary64_412 difference-of-sqr-1_binary64_389 flip3--_binary64_423 flip-+_binary64_393 flip--_binary64_394 +-commutative_binary64_349
Counts
2 → 38
Calls

4 calls:

7.0ms
(-.f64 (+.f64 1 (log.f64 n)) 1)
4.0ms
(+.f64 1 (log.f64 n))
0.0ms
(+.f64 1 (log.f64 n))
0.0ms
(-.f64 (+.f64 1 (log.f64 n)) 1)

series97.0ms (0.2%)

Counts
2 → 6
Calls

2 calls:

49.0ms
(-.f64 (+.f64 1 (log.f64 n)) 1)
48.0ms
(+.f64 1 (log.f64 n))
Compiler

Compiled 80 to 80 computations (0% saved)

simplify75.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
05019345

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 n (log.f64 n))
0.2b
(-.f64 n (*.f64 n (log.f64 n)))
0.2b
(-.f64 n (*.f64 n (log.f64 n)))
0.3b
(*.f64 n (log.f64 n))

rewrite11.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×log-prod_binary64_505
10×add-sqr-sqrt_binary64_441
8×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
6×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368 associate--r+_binary64_355
5×pow1_binary64_480
4×add-log-exp_binary64_458 associate-*r*_binary64_359 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
3×associate-*l*_binary64_360
1×pow-prod-down_binary64_490 sub-neg_binary64_412 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 flip3--_binary64_423 log-pow_binary64_508 *-commutative_binary64_350 diff-log_binary64_511 flip--_binary64_394 cancel-sign-sub-inv_binary64_385
Counts
2 → 43
Calls

4 calls:

5.0ms
(*.f64 n (log.f64 n))
4.0ms
(-.f64 n (*.f64 n (log.f64 n)))
0.0ms
(-.f64 n (*.f64 n (log.f64 n)))
0.0ms
(*.f64 n (log.f64 n))

series154.0ms (0.4%)

Counts
2 → 6
Calls

2 calls:

84.0ms
(-.f64 n (*.f64 n (log.f64 n)))
70.0ms
(*.f64 n (log.f64 n))
Compiler

Compiled 132 to 114 computations (13.6% saved)

simplify62.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
04877533
14877533

localize13.0ms (0%)

Local error

Found 6 expressions with local error:

6.1b
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (*.f64 n (log.f64 n)))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 n (log.f64 n))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 n (log.f64 n))
6.1b
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (*.f64 n (log.f64 n)))

rewrite38.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×log-prod_binary64_505
25×*-un-lft-identity_binary64_419
19×add-sqr-sqrt_binary64_441
18×associate--l+_binary64_356
15×add-cube-cbrt_binary64_454
14×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368
9×pow1_binary64_480
8×add-log-exp_binary64_458 associate-*r*_binary64_359
7×associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
6×associate--r+_binary64_355
5×distribute-lft-out_binary64_370
3×diff-log_binary64_511
2×associate-*l/_binary64_362 pow-prod-down_binary64_490 sub-neg_binary64_412 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 log-pow_binary64_508 *-commutative_binary64_350 cancel-sign-sub-inv_binary64_385
1×flip3-+_binary64_422 flip3--_binary64_423 flip-+_binary64_393 associate--l-_binary64_357 flip--_binary64_394
Counts
3 → 85
Calls

6 calls:

14.0ms
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (*.f64 n (log.f64 n)))
9.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
5.0ms
(*.f64 n (log.f64 n))
0.0ms
(*.f64 n (log.f64 n))
0.0ms
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (*.f64 n (log.f64 n)))

series151.0ms (0.4%)

Counts
3 → 11
Calls

3 calls:

71.0ms
(*.f64 n (log.f64 n))
52.0ms
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (*.f64 n (log.f64 n)))
27.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
Compiler

Compiled 386 to 321 computations (16.8% saved)

simplify123.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
049371502
149371502

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 n (sqrt.f64 (log.f64 n)))
0.1b
(sqrt.f64 (log.f64 n))
0.1b
(sqrt.f64 (log.f64 n))
0.3b
(*.f64 n (sqrt.f64 (log.f64 n)))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.4b
(*.f64 (*.f64 n (sqrt.f64 (log.f64 n))) (sqrt.f64 (log.f64 n)))
36.2b
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 (*.f64 n (sqrt.f64 (log.f64 n))) (sqrt.f64 (log.f64 n))))

rewrite43.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
25×*-un-lft-identity_binary64_419
21×add-sqr-sqrt_binary64_441
18×associate-*r*_binary64_359
16×log-prod_binary64_505 pow1_binary64_480
15×add-cube-cbrt_binary64_454
13×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
9×sqrt-prod_binary64_435
8×associate--l+_binary64_356 distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368 associate-*l*_binary64_360
6×add-log-exp_binary64_458
5×pow-prod-down_binary64_490 prod-exp_binary64_468 cbrt-unprod_binary64_452 distribute-lft-out_binary64_370
3×unswap-sqr_binary64_387 log-pow_binary64_508 *-commutative_binary64_350
2×associate-*l/_binary64_362
1×flip3-+_binary64_422 sub-neg_binary64_412 flip3--_binary64_423 flip-+_binary64_393 diff-log_binary64_511 flip--_binary64_394 cancel-sign-sub-inv_binary64_385
Counts
4 → 95
Calls

8 calls:

11.0ms
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 (*.f64 n (sqrt.f64 (log.f64 n))) (sqrt.f64 (log.f64 n))))
10.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
8.0ms
(*.f64 (*.f64 n (sqrt.f64 (log.f64 n))) (sqrt.f64 (log.f64 n)))
6.0ms
(*.f64 n (sqrt.f64 (log.f64 n)))
0.0ms
(sqrt.f64 (log.f64 n))

series265.0ms (0.6%)

Counts
4 → 14
Calls

4 calls:

104.0ms
(*.f64 n (sqrt.f64 (log.f64 n)))
82.0ms
(*.f64 (*.f64 n (sqrt.f64 (log.f64 n))) (sqrt.f64 (log.f64 n)))
52.0ms
(-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 (*.f64 n (sqrt.f64 (log.f64 n))) (sqrt.f64 (log.f64 n))))
27.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
Compiler

Compiled 492 to 391 computations (20.5% saved)

simplify86.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
054521576

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1))))
0.3b
(*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2))
0.0b
(log.f64 (cbrt.f64 (+.f64 n 1)))
0.0b
(log.f64 (cbrt.f64 (+.f64 n 1)))
0.3b
(+.f64 (*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2)) (*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1)))))
0.5b
(cbrt.f64 (+.f64 n 1))
0.5b
(cbrt.f64 (+.f64 n 1))
30.1b
(-.f64 (+.f64 (*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2)) (*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1))))) (*.f64 n (log.f64 n)))

rewrite48.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
20×*-un-lft-identity_binary64_419 log-prod_binary64_505
16×cbrt-prod_binary64_450
14×associate-+r+_binary64_351
12×add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
11×add-log-exp_binary64_458
10×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368
8×associate-*l/_binary64_362
7×flip3-+_binary64_422 flip-+_binary64_393
6×associate--r+_binary64_355
5×distribute-lft-out_binary64_370
4×frac-add_binary64_427 cbrt-div_binary64_451 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
2×pow1/3_binary64_501 sum-log_binary64_510 diff-log_binary64_511
1×associate--l+_binary64_356 sub-neg_binary64_412 flip3--_binary64_423 flip--_binary64_394 cancel-sign-sub-inv_binary64_385 +-commutative_binary64_349
Counts
4 → 78
Calls

8 calls:

17.0ms
(-.f64 (+.f64 (*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2)) (*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1))))) (*.f64 n (log.f64 n)))
14.0ms
(+.f64 (*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2)) (*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1)))))
3.0ms
(cbrt.f64 (+.f64 n 1))
3.0ms
(cbrt.f64 (+.f64 n 1))
0.0ms
(log.f64 (cbrt.f64 (+.f64 n 1)))

series199.0ms (0.5%)

Counts
4 → 17
Calls

4 calls:

82.0ms
(-.f64 (+.f64 (*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2)) (*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1))))) (*.f64 n (log.f64 n)))
54.0ms
(+.f64 (*.f64 (+.f64 n 1) (*.f64 (log.f64 (cbrt.f64 (+.f64 n 1))) 2)) (*.f64 (+.f64 n 1) (log.f64 (cbrt.f64 (+.f64 n 1)))))
33.0ms
(cbrt.f64 (+.f64 n 1))
29.0ms
(cbrt.f64 (+.f64 n 1))
Compiler

Compiled 816 to 691 computations (15.3% saved)

simplify79.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049821766
149821766

prune4.3s (10%)

Pruning

156 alts after pruning (152 fresh and 4 done)

PrunedKeptTotal
New270123393
Fresh92938
Picked000
Done246
Total281156437
Error
0b
Counts
437 → 156
Compiler

Compiled 9454 to 6304 computations (33.3% saved)

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 -1 (sqrt.f64 (+.f64 1 (log.f64 n))))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n))))
0.0b
(+.f64 1 (log.f64 n))
0.0b
(+.f64 1 (log.f64 n))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n))))
0.1b
(sqrt.f64 (+.f64 1 (log.f64 n)))
0.1b
(sqrt.f64 (+.f64 1 (log.f64 n)))
0.5b
(*.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n)))) (+.f64 -1 (sqrt.f64 (+.f64 1 (log.f64 n)))))

rewrite41.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×*-un-lft-identity_binary64_419
18×add-sqr-sqrt_binary64_441
17×distribute-lft-out_binary64_370
16×sqrt-prod_binary64_435
12×pow1_binary64_480
9×flip3-+_binary64_422 flip-+_binary64_393
8×add-cube-cbrt_binary64_454
7×associate-*l*_binary64_360
6×add-log-exp_binary64_458 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
4×sqrt-div_binary64_436 associate-*r*_binary64_359 frac-times_binary64_429 log-pow_binary64_508
2×associate-*l/_binary64_362 pow1/2_binary64_499 associate-*r/_binary64_361 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432
1×pow-prod-down_binary64_490 distribute-rgt-in_binary64_369 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 sum-log_binary64_510 distribute-lft-in_binary64_368 *-commutative_binary64_350 +-commutative_binary64_349
Counts
4 → 82
Calls

8 calls:

19.0ms
(*.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n)))) (+.f64 -1 (sqrt.f64 (+.f64 1 (log.f64 n)))))
6.0ms
(+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n))))
4.0ms
(sqrt.f64 (+.f64 1 (log.f64 n)))
4.0ms
(sqrt.f64 (+.f64 1 (log.f64 n)))
0.0ms
(+.f64 1 (log.f64 n))

series365.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

161.0ms
(*.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n)))) (+.f64 -1 (sqrt.f64 (+.f64 1 (log.f64 n)))))
72.0ms
(+.f64 1 (sqrt.f64 (+.f64 1 (log.f64 n))))
70.0ms
(sqrt.f64 (+.f64 1 (log.f64 n)))
62.0ms
(sqrt.f64 (+.f64 1 (log.f64 n)))
Compiler

Compiled 430 to 398 computations (7.4% saved)

simplify121.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (102.0ms)

IterNodesCost
049231250
149231250

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))
0.3b
(*.f64 (*.f64 n (*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))) (cbrt.f64 (log.f64 n)))
0.3b
(*.f64 n (*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n))))
0.2b
(-.f64 n (*.f64 (*.f64 n (*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))) (cbrt.f64 (log.f64 n))))
0.5b
(*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))
0.6b
(cbrt.f64 (log.f64 n))
0.6b
(cbrt.f64 (log.f64 n))
0.6b
(cbrt.f64 (log.f64 n))

rewrite21.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
36×cbrt-prod_binary64_450
23×add-sqr-sqrt_binary64_441
20×pow1_binary64_480
17×*-un-lft-identity_binary64_419
15×add-cube-cbrt_binary64_454
9×pow1/3_binary64_501 log-pow_binary64_508 swap-sqr_binary64_386
7×associate-*r*_binary64_359 associate-*l*_binary64_360
6×add-exp-log_binary64_457
4×add-log-exp_binary64_458 unswap-sqr_binary64_387 add-cbrt-cube_binary64_455
2×pow-prod-down_binary64_490 pow-sqr_binary64_392 pow-prod-up_binary64_489
1×prod-exp_binary64_468 cbrt-unprod_binary64_452 pow-plus_binary64_482 *-commutative_binary64_350 pow2_binary64_500
Counts
4 → 81
Calls

8 calls:

7.0ms
(*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))
1.0ms
(cbrt.f64 (log.f64 n))
1.0ms
(cbrt.f64 (log.f64 n))
1.0ms
(cbrt.f64 (log.f64 n))
0.0ms
(-.f64 n (*.f64 (*.f64 n (*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))) (cbrt.f64 (log.f64 n))))

series597.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

160.0ms
(*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))
151.0ms
(cbrt.f64 (log.f64 n))
149.0ms
(cbrt.f64 (log.f64 n))
137.0ms
(cbrt.f64 (log.f64 n))
Compiler

Compiled 488 to 354 computations (27.5% saved)

simplify64.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
04995799
14995799

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.2b
(*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n)))
0.2b
(*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2)))
0.1b
(*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))
0.3b
(*.f64 n (log.f64 n))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
14.5b
(/.f64 (-.f64 (*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))) (*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n)))) (+.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n))))
50.8b
(-.f64 (*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))) (*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n))))

rewrite65.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
30×*-un-lft-identity_binary64_419
28×add-sqr-sqrt_binary64_441
26×log-prod_binary64_505
24×add-cube-cbrt_binary64_454
19×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368
12×associate--r+_binary64_355
10×add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
9×times-frac_binary64_425
8×associate-*r*_binary64_359
7×associate-*l*_binary64_360
6×add-log-exp_binary64_458
3×distribute-lft-out_binary64_370 associate-/r*_binary64_363 associate-/l*_binary64_364
2×flip3-+_binary64_422 associate-*l/_binary64_362 pow-prod-down_binary64_490 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 flip3--_binary64_423 associate-/r/_binary64_365 log-pow_binary64_508 *-commutative_binary64_350 flip-+_binary64_393 flip--_binary64_394 associate-/l/_binary64_366
1×clear-num_binary64_418 sub-neg_binary64_412 div-inv_binary64_416 frac-2neg_binary64_430 diff-log_binary64_511 cancel-sign-sub-inv_binary64_385 div-exp_binary64_470 cbrt-undiv_binary64_453 div-sub_binary64_424
Counts
4 → 111
Calls

8 calls:

22.0ms
(/.f64 (-.f64 (*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))) (*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n)))) (+.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n))))
12.0ms
(-.f64 (*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))) (*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n))))
9.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
5.0ms
(*.f64 n (log.f64 n))
0.0ms
(*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))

series692.0ms (1.6%)

Counts
4 → 15
Calls

4 calls:

432.0ms
(/.f64 (-.f64 (*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))) (*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n)))) (+.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 n))))
153.0ms
(-.f64 (*.f64 (log.f64 (+.f64 n 1)) (*.f64 (log.f64 (+.f64 n 1)) (pow.f64 (+.f64 n 1) 2))) (*.f64 (*.f64 n (log.f64 n)) (*.f64 n (log.f64 n))))
78.0ms
(*.f64 n (log.f64 n))
29.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
Compiler

Compiled 1659 to 1320 computations (20.4% saved)

simplify117.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049084622
149084622

prune7.8s (18.2%)

Pruning

272 alts after pruning (264 fresh and 8 done)

PrunedKeptTotal
New185128313
Fresh11136147
Picked000
Done189
Total197272469
Error
0b
Counts
469 → 272
Compiler

Compiled 15946 to 10594 computations (33.6% saved)

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (*.f64 1 (+.f64 1 (log.f64 n))) 1)
0.0b
(+.f64 1 (log.f64 n))
0.0b
(+.f64 1 (log.f64 n))
0.0b
(-.f64 (*.f64 1 (+.f64 1 (log.f64 n))) 1)

rewrite13.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
8×*-un-lft-identity_binary64_419
5×add-log-exp_binary64_458
4×add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
3×associate-+r+_binary64_351 log-prod_binary64_505 cancel-sign-sub-inv_binary64_385 pow1_binary64_480
2×associate--l+_binary64_356 distribute-lft-out_binary64_370 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
1×flip3-+_binary64_422 sub-neg_binary64_412 distribute-rgt-in_binary64_369 sum-log_binary64_510 flip3--_binary64_423 distribute-lft-out--_binary64_371 log-pow_binary64_508 distribute-lft-in_binary64_368 flip-+_binary64_393 diff-log_binary64_511 flip--_binary64_394 +-commutative_binary64_349
Counts
2 → 33
Calls

4 calls:

7.0ms
(-.f64 (*.f64 1 (+.f64 1 (log.f64 n))) 1)
4.0ms
(+.f64 1 (log.f64 n))
0.0ms
(+.f64 1 (log.f64 n))
0.0ms
(-.f64 (*.f64 1 (+.f64 1 (log.f64 n))) 1)

series106.0ms (0.2%)

Counts
2 → 6
Calls

2 calls:

55.0ms
(+.f64 1 (log.f64 n))
51.0ms
(-.f64 (*.f64 1 (+.f64 1 (log.f64 n))) 1)
Compiler

Compiled 92 to 92 computations (0% saved)

simplify58.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
05015278

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

6.0b
(exp.f64 (log.f64 (*.f64 n (log.f64 n))))
0.7b
(log.f64 (*.f64 n (log.f64 n)))
0.3b
(*.f64 n (log.f64 n))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.7b
(log.f64 (*.f64 n (log.f64 n)))
6.0b
(exp.f64 (log.f64 (*.f64 n (log.f64 n))))
62.5b
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (exp.f64 (log.f64 (*.f64 n (log.f64 n)))))

rewrite42.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_419
19×log-prod_binary64_505
18×associate--l+_binary64_356
16×add-sqr-sqrt_binary64_441
13×pow1_binary64_480
12×add-cube-cbrt_binary64_454
9×add-log-exp_binary64_458 add-exp-log_binary64_457
8×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368
6×add-cbrt-cube_binary64_455
5×distribute-lft-out_binary64_370 exp-prod_binary64_471 log-pow_binary64_508 cancel-sign-sub-inv_binary64_385
4×associate-*r*_binary64_359 associate-*l*_binary64_360
3×pow-prod-down_binary64_490 diff-log_binary64_511
2×associate-*l/_binary64_362 sub-neg_binary64_412 rem-log-exp_binary64_460 prod-exp_binary64_468 exp-sum_binary64_465
1×flip3-+_binary64_422 difference-of-squares_binary64_388 unswap-sqr_binary64_387 cbrt-unprod_binary64_452 flip3--_binary64_423 distribute-lft-out--_binary64_371 *-commutative_binary64_350 flip-+_binary64_393 associate--l-_binary64_357 flip--_binary64_394 rem-exp-log_binary64_459
Counts
4 → 85
Calls

8 calls:

16.0ms
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (exp.f64 (log.f64 (*.f64 n (log.f64 n)))))
10.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
4.0ms
(exp.f64 (log.f64 (*.f64 n (log.f64 n))))
3.0ms
(log.f64 (*.f64 n (log.f64 n)))
0.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))

series358.0ms (0.8%)

Counts
4 → 14
Calls

4 calls:

145.0ms
(exp.f64 (log.f64 (*.f64 n (log.f64 n))))
127.0ms
(log.f64 (*.f64 n (log.f64 n)))
58.0ms
(-.f64 (-.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (*.f64 n (log.f64 1))) (exp.f64 (log.f64 (*.f64 n (log.f64 n)))))
28.0ms
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
Compiler

Compiled 655 to 551 computations (15.9% saved)

simplify90.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049291496
149291496

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b
(*.f64 n (log.f64 n))
1.2b
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
1.2b
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
1.2b
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
42.6b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))) (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))) (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))) (*.f64 n (log.f64 n)))

rewrite38.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
6×*-un-lft-identity_binary64_419 associate-*l/_binary64_362 add-log-exp_binary64_458 cbrt-div_binary64_451 add-cube-cbrt_binary64_454 log-prod_binary64_505 add-sqr-sqrt_binary64_441 associate--r+_binary64_355
4×add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
3×flip3-+_binary64_422 pow1/3_binary64_501 distribute-rgt-in_binary64_369 cbrt-prod_binary64_450 distribute-lft-in_binary64_368 flip-+_binary64_393
1×sub-neg_binary64_412 flip3--_binary64_423 diff-log_binary64_511 flip--_binary64_394 cancel-sign-sub-inv_binary64_385
Counts
4 → 51
Calls

8 calls:

17.0ms
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))) (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))) (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))) (*.f64 n (log.f64 n)))
5.0ms
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
5.0ms
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
5.0ms
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
0.0ms
(*.f64 n (log.f64 n))

series262.0ms (0.6%)

Counts
4 → 16
Calls

4 calls:

69.0ms
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
68.0ms
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
67.0ms
(cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))
58.0ms
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))) (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))) (cbrt.f64 (*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))))) (*.f64 n (log.f64 n)))
Compiler

Compiled 1394 to 1177 computations (15.6% saved)

simplify132.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (113.0ms)

IterNodesCost
048661172
148661172

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 n (*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n))))
0.2b
(-.f64 n (*.f64 (*.f64 n (*.f64 (cbrt.f64 (log.f64 n)) (cbrt.f64 (log.f64 n)))) (*.f64 (cbrt.f64 (sqrt.f64 (log.f64 n))) (cbrt.f64 (sqrt.f64 (log.f64 n))))))
0.1b
(sqrt.f64 (log.f64 n))
0.1b
(sqrt.f64 (log.f64 n))
0.6b
(cbrt.f64 (log.f64 n))
0.6b
(cbrt.f64 (log.f64 n))
0.6b
(cbrt.f64 (sqrt.f64 (log.f64 n)))
0.6b
(cbrt.f64 (sqrt.f64 (log.f64 n)))

rewrite11.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
22×cbrt-prod_binary64_450
10×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
8×sqrt-prod_binary64_435 pow1_binary64_480
4×pow1/3_binary64_501 add-log-exp_binary64_458 log-pow_binary64_508 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
Counts
4 → 54
Calls

8 calls:

2.0ms
(cbrt.f64 (sqrt.f64 (log.f64 n)))
2.0ms
(cbrt.f64 (sqrt.f64 (log.f64 n)))
1.0ms
(cbrt.f64 (log.f64 n))
1.0ms
(cbrt.f64 (log.f64 n))
0.0ms
(sqrt.f64 (log.f64 n))

series586.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

150.0ms
(cbrt.f64 (sqrt.f64 (log.f64 n)))
149.0ms
(cbrt.f64 (log.f64 n))
143.0ms
(cbrt.f64 (log.f64 n))
143.0ms
(cbrt.f64 (sqrt.f64 (log.f64 n)))
Compiler

Compiled 636 to 424 computations (33.3% saved)

simplify93.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
04952626
14952626

prune8.7s (20.4%)

Pruning

339 alts after pruning (327 fresh and 12 done)

PrunedKeptTotal
New19081271
Fresh13246259
Picked000
Done11213
Total204339543
Error
0b
Counts
543 → 339
Compiler

Compiled 5078 to 2892 computations (43% saved)

simplify637.0ms (1.5%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
0502927304

regimes2.0s (4.7%)

Compiler

Compiled 25154 to 18200 computations (27.6% saved)

bsearch0.0ms (0%)

regimes8.0ms (0%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
054
154

end0.0ms (0%)

sample12.6s (29.6%)

Algorithm
1×intervals
Results
1.2s4217×body1024valid
394.0ms2068×body512valid
204.0ms462×body2048valid
128.0ms1092×body256valid
104.0ms8000×pre128true
9.0ms161×body128valid
Compiler

Compiled 12536 to 9076 computations (27.6% saved)

Pareto

0.0

Profiling

Loading profile data...