Details

Time bar (total: 59.4s)

analyze3.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%50%50%2
25%25%50%3
25%12.5%62.5%4
25%6.2%68.8%5
25%3.1%71.9%6
25%1.6%73.5%7
25%0.8%74.2%8
25%0.4%74.6%9
25%0.2%74.8%10
25%0.1%74.9%11
25%0%75%12
25%0%75%13
25%0%75%14
Compiler

Compiled 7 to 5 computations (28.6% saved)

sample15.0ms (0%)

Algorithm
intervals
Results
10.0ms256×body128valid
Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify300.0ms (0.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (197.0ms)

IterNodesCost
0496510
1496510

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 1
Compiler

Compiled 6 to 4 computations (33.3% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

rewrite10.0ms (0%)

Algorithm
rewrite-expression-head
Rules
11×log-prod_binary64_2551
10×*-un-lft-identity_binary64_2465 pow1_binary64_2526
log-pow_binary64_2554 add-sqr-sqrt_binary64_2487
add-cube-cbrt_binary64_2500
associate--r+_binary64_2401 distribute-lft-out--_binary64_2417 cancel-sign-sub-inv_binary64_2431
add-exp-log_binary64_2503 associate--l+_binary64_2402
add-log-exp_binary64_2504 add-cbrt-cube_binary64_2501
difference-of-squares_binary64_2434 flip--_binary64_2440 sub-neg_binary64_2458 diff-log_binary64_2557 flip3--_binary64_2469 rem-log-exp_binary64_2506
Counts
2 → 40
Calls

4 calls:

6.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
1.0ms
(log.f64 (log.f64 x))
0.0ms
(log.f64 (log.f64 x))
0.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

series306.0ms (0.5%)

Counts
2 → 6
Calls

2 calls:

178.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
128.0ms
(log.f64 (log.f64 x))
Compiler

Compiled 122 to 106 computations (13.1% saved)

simplify65.0ms (0.1%)

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
05070484

prune108.0ms (0.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New252146
Fresh000
Picked000
Done011
Total252247
Error
0b
Counts
47 → 22
Compiler

Compiled 565 to 248 computations (56.1% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(/.f64 x (log.f64 x))
0.2b
(/.f64 x (log.f64 x))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
12×times-frac_binary64_2471
10×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
pow1_binary64_2526
associate-/r*_binary64_2409 log-pow_binary64_2554
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 associate-/l*_binary64_2410
add-log-exp_binary64_2504 clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-exp_binary64_2516 div-inv_binary64_2462 frac-2neg_binary64_2476
Counts
1 → 31
Calls

2 calls:

3.0ms
(/.f64 x (log.f64 x))
0.0ms
(/.f64 x (log.f64 x))

series105.0ms (0.2%)

Counts
1 → 3
Calls

1 calls:

105.0ms
(/.f64 x (log.f64 x))
Compiler

Compiled 48 to 42 computations (12.5% saved)

simplify52.0ms (0.1%)

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05262380

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(+.f64 (log.f64 x) (neg.f64 (log.f64 (log.f64 x))))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.3b
(+.f64 (log.f64 x) (neg.f64 (log.f64 (log.f64 x))))

rewrite11.0ms (0%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64_2465
11×log-prod_binary64_2551
10×pow1_binary64_2526
log-pow_binary64_2554
distribute-lft-out_binary64_2416
add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
distribute-rgt-neg-in_binary64_2423 associate-+r+_binary64_2397 distribute-neg-in_binary64_2426
add-log-exp_binary64_2504 associate-+l+_binary64_2398 add-exp-log_binary64_2503
sum-log_binary64_2556 add-cbrt-cube_binary64_2501
flip3-+_binary64_2468 neg-log_binary64_2558 +-commutative_binary64_2395 associate-+r-_binary64_2399 flip-+_binary64_2439 unsub-neg_binary64_2459 rem-log-exp_binary64_2506 neg-sub0_binary64_2460
Counts
2 → 40
Calls

4 calls:

7.0ms
(+.f64 (log.f64 x) (neg.f64 (log.f64 (log.f64 x))))
1.0ms
(log.f64 (log.f64 x))
0.0ms
(log.f64 (log.f64 x))
0.0ms
(+.f64 (log.f64 x) (neg.f64 (log.f64 (log.f64 x))))

series284.0ms (0.5%)

Counts
2 → 6
Calls

2 calls:

156.0ms
(+.f64 (log.f64 x) (neg.f64 (log.f64 (log.f64 x))))
128.0ms
(log.f64 (log.f64 x))
Compiler

Compiled 128 to 112 computations (12.5% saved)

simplify102.0ms (0.2%)

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
04903458
14903458

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

1.1b
(exp.f64 (log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.0b
(log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
1.1b
(exp.f64 (log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))

rewrite24.0ms (0%)

Algorithm
rewrite-expression-head
Rules
27×log-prod_binary64_2551
23×*-un-lft-identity_binary64_2465
22×pow1_binary64_2526
18×log-pow_binary64_2554
17×add-sqr-sqrt_binary64_2487
12×distribute-lft-out--_binary64_2417
11×add-cube-cbrt_binary64_2500
exp-sum_binary64_2511
add-exp-log_binary64_2503
associate--r+_binary64_2401 log-div_binary64_2552 add-log-exp_binary64_2504 add-cbrt-cube_binary64_2501 cancel-sign-sub-inv_binary64_2431 exp-prod_binary64_2517
difference-of-squares_binary64_2434 flip--_binary64_2440 associate--l+_binary64_2402 flip3--_binary64_2469
rem-log-exp_binary64_2506 exp-diff_binary64_2513
sub-neg_binary64_2458 diff-log_binary64_2557 rem-exp-log_binary64_2505
Counts
4 → 81
Calls

8 calls:

6.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
6.0ms
(exp.f64 (log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))
4.0ms
(log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
1.0ms
(log.f64 (log.f64 x))
0.0ms
(log.f64 (log.f64 x))

series844.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

285.0ms
(exp.f64 (log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))
267.0ms
(log.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
164.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
128.0ms
(log.f64 (log.f64 x))
Compiler

Compiled 306 to 274 computations (10.5% saved)

simplify118.0ms (0.2%)

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
048821248
148821248

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(sqrt.f64 (log.f64 x))
0.2b
(sqrt.f64 (log.f64 x))
0.1b
(log.f64 (sqrt.f64 (log.f64 x)))
0.1b
(log.f64 (sqrt.f64 (log.f64 x)))
0.1b
(log.f64 (sqrt.f64 (log.f64 x)))
0.2b
(sqrt.f64 (log.f64 x))
0.2b
(sqrt.f64 (log.f64 x))
0.3b
(-.f64 (log.f64 x) (+.f64 (log.f64 (sqrt.f64 (log.f64 x))) (log.f64 (sqrt.f64 (log.f64 x)))))

rewrite31.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
41×log-pow_binary64_2554
40×pow1_binary64_2526
35×*-un-lft-identity_binary64_2465
26×cancel-sign-sub-inv_binary64_2431
18×add-sqr-sqrt_binary64_2487
16×distribute-lft-out_binary64_2416
14×add-cube-cbrt_binary64_2500
12×sqrt-prod_binary64_2481
10×log-prod_binary64_2551 distribute-lft-out--_binary64_2417 distribute-rgt-out_binary64_2418
pow1/2_binary64_2545 sqrt-pow1_binary64_2483
add-log-exp_binary64_2504 add-exp-log_binary64_2503
add-cbrt-cube_binary64_2501
associate--l+_binary64_2402
distribute-lft1-in_binary64_2420 distribute-rgt1-in_binary64_2421 rem-sqrt-square_binary64_2478 diff-log_binary64_2557
associate--r+_binary64_2401 difference-of-squares_binary64_2434 flip--_binary64_2440 sum-log_binary64_2556 count-2_binary64_2413 sub-neg_binary64_2458 flip3--_binary64_2469 rem-log-exp_binary64_2506
Counts
4 → 99
Calls

8 calls:

17.0ms
(-.f64 (log.f64 x) (+.f64 (log.f64 (sqrt.f64 (log.f64 x))) (log.f64 (sqrt.f64 (log.f64 x)))))
2.0ms
(log.f64 (sqrt.f64 (log.f64 x)))
1.0ms
(sqrt.f64 (log.f64 x))
1.0ms
(sqrt.f64 (log.f64 x))
0.0ms
(log.f64 (sqrt.f64 (log.f64 x)))

series423.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

187.0ms
(-.f64 (log.f64 x) (+.f64 (log.f64 (sqrt.f64 (log.f64 x))) (log.f64 (sqrt.f64 (log.f64 x)))))
120.0ms
(log.f64 (sqrt.f64 (log.f64 x)))
59.0ms
(sqrt.f64 (log.f64 x))
57.0ms
(sqrt.f64 (log.f64 x))
Compiler

Compiled 352 to 272 computations (22.7% saved)

simplify94.0ms (0.2%)

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
048971011
148971011

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.1b
(sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.1b
(sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.5b
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))

rewrite54.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity_binary64_2465
86×sqrt-prod_binary64_2481
84×pow1_binary64_2526
64×log-pow_binary64_2554
60×distribute-lft-out--_binary64_2417
48×add-sqr-sqrt_binary64_2487
33×swap-sqr_binary64_2432
19×add-cube-cbrt_binary64_2500
14×log-prod_binary64_2551 sqrt-div_binary64_2482
11×associate-*r*_binary64_2405 associate-*l*_binary64_2406
flip--_binary64_2440 pow1/2_binary64_2545 flip3--_binary64_2469 sqrt-pow1_binary64_2483
associate--r+_binary64_2401 cancel-sign-sub-inv_binary64_2431
difference-of-squares_binary64_2434
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 associate--l+_binary64_2402
pow-prod-up_binary64_2535
add-log-exp_binary64_2504 frac-times_binary64_2475 unswap-sqr_binary64_2433
rem-sqrt-square_binary64_2478 pow-prod-down_binary64_2536 pow-sqr_binary64_2438
associate-*l/_binary64_2408 associate-*r/_binary64_2407 sub-neg_binary64_2458 diff-log_binary64_2557
sqr-abs_binary64_2480 *-commutative_binary64_2396 pow-plus_binary64_2528 sqrt-unprod_binary64_2485 rem-square-sqrt_binary64_2477 pow2_binary64_2546 prod-exp_binary64_2514 cbrt-unprod_binary64_2498
Counts
4 → 167
Calls

8 calls:

16.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))
6.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
6.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
4.0ms
(sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.0ms
(log.f64 (log.f64 x))

series699.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

195.0ms
(sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))))
177.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
169.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))))
158.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
Compiler

Compiled 440 to 330 computations (25% saved)

simplify82.0ms (0.1%)

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
051002590

prune2.2s (3.7%)

Pruning

124 alts after pruning (119 fresh and 5 done)

PrunedKeptTotal
New356107463
Fresh41216
Picked000
Done156
Total361124485
Error
0b
Counts
485 → 124
Compiler

Compiled 5396 to 1904 computations (64.7% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(/.f64 x (log.f64 x))
0.2b
(/.f64 x (log.f64 x))

rewrite7.0ms (0%)

Algorithm
rewrite-expression-head
Rules
12×times-frac_binary64_2471
10×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
pow1_binary64_2526
associate-/r*_binary64_2409 log-pow_binary64_2554
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 associate-/l*_binary64_2410
add-log-exp_binary64_2504 clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-exp_binary64_2516 div-inv_binary64_2462 frac-2neg_binary64_2476
Counts
1 → 31
Calls

2 calls:

4.0ms
(/.f64 x (log.f64 x))
0.0ms
(/.f64 x (log.f64 x))

series100.0ms (0.2%)

Counts
1 → 3
Calls

1 calls:

100.0ms
(/.f64 x (log.f64 x))
Compiler

Compiled 60 to 54 computations (10% saved)

simplify53.0ms (0.1%)

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
05262380

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (log.f64 x) x)
0.3b
(/.f64 1 (/.f64 (log.f64 x) x))
0.3b
(/.f64 1 (/.f64 (log.f64 x) x))
0.3b
(/.f64 (log.f64 x) x)

rewrite21.0ms (0%)

Algorithm
rewrite-expression-head
Rules
108×times-frac_binary64_2471
60×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
19×associate-/r*_binary64_2409 pow1_binary64_2526
16×log-pow_binary64_2554
15×add-exp-log_binary64_2503
add-cbrt-cube_binary64_2501
div-exp_binary64_2516
associate-/l*_binary64_2410
div-inv_binary64_2462
cbrt-undiv_binary64_2499
add-log-exp_binary64_2504 rec-exp_binary64_2515 clear-num_binary64_2464 frac-2neg_binary64_2476 1-exp_binary64_2509
inv-pow_binary64_2550 pow-flip_binary64_2539 associate-/r/_binary64_2411
Counts
2 → 119
Calls

4 calls:

7.0ms
(/.f64 1 (/.f64 (log.f64 x) x))
4.0ms
(/.f64 (log.f64 x) x)
0.0ms
(/.f64 1 (/.f64 (log.f64 x) x))
0.0ms
(/.f64 (log.f64 x) x)

series178.0ms (0.3%)

Counts
2 → 6
Calls

2 calls:

95.0ms
(/.f64 1 (/.f64 (log.f64 x) x))
82.0ms
(/.f64 (log.f64 x) x)
Compiler

Compiled 112 to 100 computations (10.7% saved)

simplify78.0ms (0.1%)

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
052581787

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.0b
(log.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3)))
0.0b
(log.f64 (log.f64 x))
0.3b
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.5b
(cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))
0.8b
(pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3)
1.1b
(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))))

rewrite44.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity_binary64_2465
44×cbrt-prod_binary64_2496
36×pow1_binary64_2526
32×log-prod_binary64_2551 log-pow_binary64_2554 add-sqr-sqrt_binary64_2487
28×distribute-lft-out--_binary64_2417
25×exp-sum_binary64_2511
24×cube-prod_binary64_2493 unpow-prod-down_binary64_2544
18×add-cube-cbrt_binary64_2500
difference-of-squares_binary64_2434
cube-div_binary64_2494
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 exp-prod_binary64_2517
associate--r+_binary64_2401 add-log-exp_binary64_2504 flip--_binary64_2440 cbrt-div_binary64_2497 cancel-sign-sub-inv_binary64_2431 flip3--_binary64_2469
unpow3_binary64_2531 cube-mult_binary64_2495 sqr-pow_binary64_2437 associate--l+_binary64_2402 pow-unpow_binary64_2542
log-div_binary64_2552 pow1/3_binary64_2547 exp-diff_binary64_2513
rem-cube-cbrt_binary64_2488 pow-exp_binary64_2533 sub-neg_binary64_2458 pow-to-exp_binary64_2534 diff-log_binary64_2557 pow-pow_binary64_2537 rem-exp-log_binary64_2505 rem-cbrt-cube_binary64_2489
Counts
4 → 135
Calls

8 calls:

11.0ms
(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))))
7.0ms
(cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))
6.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
6.0ms
(pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3)
0.0ms
(log.f64 (log.f64 x))

series869.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

287.0ms
(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))))
239.0ms
(pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3)
185.0ms
(cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))
157.0ms
(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
Compiler

Compiled 362 to 330 computations (8.8% saved)

simplify94.0ms (0.2%)

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049562393
149562393

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(+.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.1b
(sqrt.f64 (log.f64 (log.f64 x)))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.3b
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4))
0.3b
(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.5b
(pow.f64 (log.f64 x) 2)
1.0b
(pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)

rewrite88.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
221×add-sqr-sqrt_binary64_2487
144×difference-of-squares_binary64_2434
143×*-un-lft-identity_binary64_2465
140×times-frac_binary64_2471
126×unpow-prod-down_binary64_2544
94×pow1_binary64_2526
87×log-pow_binary64_2554
84×distribute-lft-out_binary64_2416
75×sqr-pow_binary64_2437
44×sqrt-prod_binary64_2481
41×add-cube-cbrt_binary64_2500
37×unpow2_binary64_2530
20×associate-/l*_binary64_2410
11×cancel-sign-sub-inv_binary64_2431
distribute-lft-out--_binary64_2417
add-exp-log_binary64_2503
associate-/r*_binary64_2409
add-log-exp_binary64_2504 add-cbrt-cube_binary64_2501 pow-unpow_binary64_2542
pow-pow_binary64_2537
flip--_binary64_2440 associate-/l/_binary64_2412 pow-exp_binary64_2533 pow-to-exp_binary64_2534 associate-/r/_binary64_2411 flip3--_binary64_2469
flip3-+_binary64_2468 sqrt-pow2_binary64_2484 pow1/2_binary64_2545 flip-+_binary64_2439 clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-sub_binary64_2470 sub-neg_binary64_2458 div-exp_binary64_2516 div-inv_binary64_2462 diff-log_binary64_2557 frac-2neg_binary64_2476 sqrt-pow1_binary64_2483
Counts
4 → 266
Calls

8 calls:

23.0ms
(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
18.0ms
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4))
4.0ms
(pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)
2.0ms
(pow.f64 (log.f64 x) 2)
0.0ms
(log.f64 (log.f64 x))

series971.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

493.0ms
(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
240.0ms
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4))
169.0ms
(pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)
69.0ms
(pow.f64 (log.f64 x) 2)
Compiler

Compiled 582 to 450 computations (22.7% saved)

simplify140.0ms (0.2%)

Algorithm
egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049228459
149228459

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
0.0b
(log.f64 (cbrt.f64 x))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))))
0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite54.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
46×pow1_binary64_2526
42×*-un-lft-identity_binary64_2465
36×add-sqr-sqrt_binary64_2487
30×sqrt-prod_binary64_2481
27×associate-*r*_binary64_2405
26×log-pow_binary64_2554
22×cbrt-prod_binary64_2496
18×add-cube-cbrt_binary64_2500
17×associate-*l*_binary64_2406
16×distribute-lft-out--_binary64_2417
15×distribute-lft-out_binary64_2416
12×sqrt-div_binary64_2482
10×pow-prod-down_binary64_2536
add-exp-log_binary64_2503 unswap-sqr_binary64_2433 pow1/3_binary64_2547
swap-sqr_binary64_2432 add-cbrt-cube_binary64_2501
add-log-exp_binary64_2504 frac-times_binary64_2475
flip3-+_binary64_2468 flip--_binary64_2440 flip-+_binary64_2439 flip3--_binary64_2469
associate-*l/_binary64_2408 *-commutative_binary64_2396 pow1/2_binary64_2545 associate-*r/_binary64_2407 prod-exp_binary64_2514 sqrt-pow1_binary64_2483 pow-sqr_binary64_2438 pow-prod-up_binary64_2535 cbrt-unprod_binary64_2498
difference-of-squares_binary64_2434 pow-plus_binary64_2528 sqrt-unprod_binary64_2485 pow2_binary64_2546
Counts
4 → 120
Calls

8 calls:

30.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))))
7.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(log.f64 (cbrt.f64 x))

series932.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

670.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))))
107.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
84.0ms
(cbrt.f64 x)
71.0ms
(cbrt.f64 x)
Compiler

Compiled 664 to 484 computations (27.1% saved)

simplify94.0ms (0.2%)

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
048921954
148921954

prune8.5s (14.3%)

Pruning

278 alts after pruning (268 fresh and 10 done)

PrunedKeptTotal
New544172716
Fresh1896114
Picked000
Done01010
Total562278840
Error
0b
Counts
840 → 278
Compiler

Compiled 13440 to 5734 computations (57.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (neg.f64 (log.f64 x)) x)
0.3b
(/.f64 -1 (/.f64 (neg.f64 (log.f64 x)) x))
0.3b
(/.f64 -1 (/.f64 (neg.f64 (log.f64 x)) x))
0.3b
(/.f64 (neg.f64 (log.f64 x)) x)

rewrite47.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
300×times-frac_binary64_2471
156×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
64×distribute-lft-neg-in_binary64_2422 distribute-rgt-neg-in_binary64_2423
43×associate-/r*_binary64_2409
34×pow1_binary64_2526
32×log-pow_binary64_2554
16×neg-mul-1_binary64_2461
15×associate-/l*_binary64_2410
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
div-inv_binary64_2462
cbrt-undiv_binary64_2499 div-exp_binary64_2516
add-log-exp_binary64_2504 clear-num_binary64_2464 frac-2neg_binary64_2476
div-sub_binary64_2470 associate-/r/_binary64_2411 distribute-frac-neg_binary64_2428 neg-sub0_binary64_2460
Counts
2 → 243
Calls

4 calls:

12.0ms
(/.f64 -1 (/.f64 (neg.f64 (log.f64 x)) x))
8.0ms
(/.f64 (neg.f64 (log.f64 x)) x)
0.0ms
(/.f64 -1 (/.f64 (neg.f64 (log.f64 x)) x))
0.0ms
(/.f64 (neg.f64 (log.f64 x)) x)

series185.0ms (0.3%)

Counts
2 → 6
Calls

2 calls:

107.0ms
(/.f64 -1 (/.f64 (neg.f64 (log.f64 x)) x))
78.0ms
(/.f64 (neg.f64 (log.f64 x)) x)
Compiler

Compiled 112 to 100 computations (10.7% saved)

simplify195.0ms (0.3%)

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 0 (140.0ms)

IterNodesCost
048544967
148544967

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (log.f64 x) (/.f64 1 x))
0.3b
(/.f64 1 (*.f64 (log.f64 x) (/.f64 1 x)))
0.3b
(/.f64 1 (*.f64 (log.f64 x) (/.f64 1 x)))
0.4b
(*.f64 (log.f64 x) (/.f64 1 x))

rewrite22.0ms (0%)

Algorithm
rewrite-expression-head
Rules
46×add-exp-log_binary64_2503
19×add-sqr-sqrt_binary64_2487
18×div-exp_binary64_2516
16×add-cbrt-cube_binary64_2501 prod-exp_binary64_2514
14×times-frac_binary64_2471
13×*-un-lft-identity_binary64_2465 associate-*r*_binary64_2405
12×add-cube-cbrt_binary64_2500
rec-exp_binary64_2515 1-exp_binary64_2509
pow1_binary64_2526
cbrt-undiv_binary64_2499
associate-*l*_binary64_2406 cbrt-unprod_binary64_2498
unswap-sqr_binary64_2433 associate-/l*_binary64_2410
add-log-exp_binary64_2504 pow-flip_binary64_2539 associate-*r/_binary64_2407 un-div-inv_binary64_2463 div-inv_binary64_2462 associate-/r/_binary64_2411 pow-prod-down_binary64_2536
*-commutative_binary64_2396 associate-/r*_binary64_2409 log-pow_binary64_2554 inv-pow_binary64_2550 clear-num_binary64_2464 frac-2neg_binary64_2476
Counts
2 → 77
Calls

4 calls:

9.0ms
(*.f64 (log.f64 x) (/.f64 1 x))
7.0ms
(/.f64 1 (*.f64 (log.f64 x) (/.f64 1 x)))
0.0ms
(/.f64 1 (*.f64 (log.f64 x) (/.f64 1 x)))
0.0ms
(*.f64 (log.f64 x) (/.f64 1 x))

series195.0ms (0.3%)

Counts
2 → 6
Calls

2 calls:

105.0ms
(/.f64 1 (*.f64 (log.f64 x) (/.f64 1 x)))
89.0ms
(*.f64 (log.f64 x) (/.f64 1 x))
Compiler

Compiled 112 to 100 computations (10.7% saved)

simplify64.0ms (0.1%)

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
04891704
14891704

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2))
0.3b
(+.f64 (log.f64 x) (log.f64 (log.f64 x)))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.3b
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2))
0.3b
(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
0.5b
(pow.f64 (log.f64 (log.f64 x)) 2)
0.5b
(pow.f64 (log.f64 x) 2)

rewrite87.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
197×*-un-lft-identity_binary64_2465
187×add-sqr-sqrt_binary64_2487
168×times-frac_binary64_2471
156×unpow-prod-down_binary64_2544
145×pow1_binary64_2526
144×difference-of-squares_binary64_2434
139×log-pow_binary64_2554
100×distribute-lft-out_binary64_2416
75×unpow2_binary64_2530 sqr-pow_binary64_2437
45×distribute-lft-out--_binary64_2417
43×add-cube-cbrt_binary64_2500
24×associate-/l*_binary64_2410
cancel-sign-sub-inv_binary64_2431
add-exp-log_binary64_2503
associate-/r*_binary64_2409
add-log-exp_binary64_2504 add-cbrt-cube_binary64_2501 pow-unpow_binary64_2542
flip--_binary64_2440 associate-/l/_binary64_2412 pow-exp_binary64_2533 pow-to-exp_binary64_2534 pow-pow_binary64_2537 associate-/r/_binary64_2411 flip3--_binary64_2469
flip3-+_binary64_2468 flip-+_binary64_2439 clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-sub_binary64_2470 sub-neg_binary64_2458 div-exp_binary64_2516 div-inv_binary64_2462 diff-log_binary64_2557 frac-2neg_binary64_2476
Counts
4 → 295
Calls

8 calls:

22.0ms
(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
10.0ms
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2))
3.0ms
(pow.f64 (log.f64 x) 2)
2.0ms
(pow.f64 (log.f64 (log.f64 x)) 2)
0.0ms
(log.f64 (log.f64 x))

series922.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

488.0ms
(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
228.0ms
(-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (log.f64 (log.f64 x)) 2))
127.0ms
(pow.f64 (log.f64 (log.f64 x)) 2)
79.0ms
(pow.f64 (log.f64 x) 2)
Compiler

Compiled 624 to 492 computations (21.2% saved)

simplify158.0ms (0.3%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049908802
149908802

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sqrt.f64 (log.f64 x)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 (log.f64 x)) (cbrt.f64 x))))
0.2b
(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sqrt.f64 (log.f64 x)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))))
0.2b
(sqrt.f64 (log.f64 x))
0.2b
(sqrt.f64 (log.f64 x))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite19.0ms (0%)

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod_binary64_2496
23×add-sqr-sqrt_binary64_2487
15×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500
11×pow1_binary64_2526
pow1/3_binary64_2547
swap-sqr_binary64_2432 add-exp-log_binary64_2503 associate-*r*_binary64_2405 associate-*l*_binary64_2406
add-log-exp_binary64_2504 unswap-sqr_binary64_2433 add-cbrt-cube_binary64_2501
pow-prod-down_binary64_2536 pow-sqr_binary64_2438 pow-prod-up_binary64_2535
*-commutative_binary64_2396 pow-plus_binary64_2528 pow2_binary64_2546 prod-exp_binary64_2514 cbrt-unprod_binary64_2498
Counts
4 → 73
Calls

8 calls:

8.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(sqrt.f64 (log.f64 x))

series337.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

102.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
80.0ms
(cbrt.f64 x)
80.0ms
(cbrt.f64 x)
74.0ms
(cbrt.f64 x)
Compiler

Compiled 682 to 526 computations (22.9% saved)

simplify81.0ms (0.1%)

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
04873548
14873548

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (log.f64 x))
0.0b
(log.f64 (cbrt.f64 x))
0.0b
(log.f64 (*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3) (sqrt.f64 (cbrt.f64 x))))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 (*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3) (sqrt.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))))
0.8b
(pow.f64 (sqrt.f64 (cbrt.f64 x)) 3)

rewrite51.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
37×sqrt-prod_binary64_2481
36×*-un-lft-identity_binary64_2465
27×add-sqr-sqrt_binary64_2487 pow1_binary64_2526
17×log-pow_binary64_2554 add-cube-cbrt_binary64_2500
16×associate-*r*_binary64_2405
12×distribute-lft-out--_binary64_2417 sqrt-div_binary64_2482 cbrt-prod_binary64_2496
11×associate-*l*_binary64_2406
10×distribute-lft-out_binary64_2416
cube-prod_binary64_2493 unpow-prod-down_binary64_2544
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
add-log-exp_binary64_2504 frac-times_binary64_2475 unswap-sqr_binary64_2433 pow-pow_binary64_2537 sqrt-pow1_binary64_2483
flip3-+_binary64_2468 flip--_binary64_2440 pow1/2_binary64_2545 flip-+_binary64_2439 pow1/3_binary64_2547 pow-prod-down_binary64_2536 pow-unpow_binary64_2542 flip3--_binary64_2469
associate-*l/_binary64_2408 associate-*r/_binary64_2407
rem-cube-cbrt_binary64_2488 difference-of-squares_binary64_2434 unpow3_binary64_2531 *-commutative_binary64_2396 sqrt-pow2_binary64_2484 sqrt-unprod_binary64_2485 pow-exp_binary64_2533 cube-mult_binary64_2495 pow-to-exp_binary64_2534 sqr-pow_binary64_2437 prod-exp_binary64_2514 cbrt-unprod_binary64_2498
Counts
4 → 114
Calls

8 calls:

30.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 (*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3) (sqrt.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))))
5.0ms
(pow.f64 (sqrt.f64 (cbrt.f64 x)) 3)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(log.f64 (*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3) (sqrt.f64 (cbrt.f64 x))))

series966.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

688.0ms
(*.f64 (sqrt.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 (*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3) (sqrt.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))))
116.0ms
(pow.f64 (sqrt.f64 (cbrt.f64 x)) 3)
82.0ms
(cbrt.f64 x)
80.0ms
(cbrt.f64 x)
Compiler

Compiled 722 to 524 computations (27.4% saved)

simplify74.0ms (0.1%)

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
048991965
148991965

prune21.9s (36.9%)

Pruning

398 alts after pruning (384 fresh and 14 done)

PrunedKeptTotal
New710140850
Fresh19244263
Picked000
Done11415
Total7303981128
Error
0b
Counts
1128 → 398
Compiler

Compiled 9812 to 3761 computations (61.7% saved)

simplify478.0ms (0.8%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0498929949
1498929949

regimes4.7s (7.9%)

Compiler

Compiled 43556 to 25296 computations (41.9% saved)

bsearch0.0ms (0%)

regimes7.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch1.0ms (0%)

Compiler

Compiled 6 to 6 computations (0% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
179

end0.0ms (0%)

sample10.5s (17.6%)

Algorithm
intervals
Results
318.0ms8000×body128valid
0.0msbody128nan
Compiler

Compiled 12340 to 7264 computations (41.1% saved)

Pareto

0.0

Profiling

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