Details

Time bar (total: 29.3s)

analyze45.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14
Compiler

Compiled 63 to 34 computations (46% saved)

sample42.0ms (0.1%)

Algorithm
intervals
Results
21.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify136.0ms (0.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0539579

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
54.7b
Counts
2 → 1
Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(*.f64 i (+.f64 (+.f64 alpha beta) i))
0.0b
(*.f64 i (+.f64 (+.f64 alpha beta) i))
0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
40.1b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
46.2b
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite161.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
86×times-frac_binary64_2471
66×flip3-+_binary64_2468 flip-+_binary64_2439 associate-/r/_binary64_2411
61×add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
46×add-sqr-sqrt_binary64_2487
44×*-un-lft-identity_binary64_2465 frac-times_binary64_2475
34×associate-*r/_binary64_2407
30×add-cube-cbrt_binary64_2500
28×difference-of-squares_binary64_2434
22×associate-*l/_binary64_2408 prod-exp_binary64_2514 cbrt-unprod_binary64_2498
19×cbrt-undiv_binary64_2499 div-exp_binary64_2516
16×pow1_binary64_2526
14×difference-of-sqr-1_binary64_2435 associate-/l*_binary64_2410
associate-/l/_binary64_2412 div-inv_binary64_2462
associate-/r*_binary64_2409
associate-*r*_binary64_2405
add-log-exp_binary64_2504 pow-prod-down_binary64_2536 associate-*l*_binary64_2406
swap-sqr_binary64_2432
distribute-lft-in_binary64_2414 *-commutative_binary64_2396 clear-num_binary64_2464 distribute-rgt-in_binary64_2415 frac-2neg_binary64_2476
pow-plus_binary64_2528 flip--_binary64_2440 unswap-sqr_binary64_2433 pow2_binary64_2546 flip3--_binary64_2469 pow-sqr_binary64_2438 pow-prod-up_binary64_2535
Counts
4 → 228
Calls

8 calls:

45.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
30.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
14.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
14.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(*.f64 i (+.f64 (+.f64 alpha beta) i))

series10.2s (34.8%)

Counts
4 → 91
Calls

4 calls:

8.7s
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
717.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
495.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
261.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 17576 to 12294 computations (30.1% saved)

simplify221.0ms (0.8%)

Algorithm
egg-herbie
Counts
319 → 319
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0582725176

prune1.2s (4.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3127319
Fresh000
Picked101
Done000
Total3137320
Error
8.8b
Counts
320 → 7
Compiler

Compiled 24343 to 10129 computations (58.4% saved)

localize0.0ms (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

prune9.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done000
Total077
Error
8.8b
Counts
7 → 7
Compiler

Compiled 252 to 144 computations (42.9% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.0b
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.0b
(*.f64 i (+.f64 i (+.f64 alpha beta)))
0.0b
(*.f64 i (+.f64 i (+.f64 alpha beta)))
0.0b
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.1b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
37.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
38.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite277.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
414×times-frac_binary64_2471
314×add-sqr-sqrt_binary64_2487
280×*-un-lft-identity_binary64_2465
169×add-cube-cbrt_binary64_2500
111×associate-*r*_binary64_2405
70×add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
62×difference-of-squares_binary64_2434
48×associate-/r/_binary64_2411
42×associate-*l*_binary64_2406
33×cbrt-undiv_binary64_2499 div-exp_binary64_2516
31×difference-of-sqr-1_binary64_2435 distribute-lft-out--_binary64_2417
24×flip3-+_binary64_2468 flip-+_binary64_2439 div-inv_binary64_2462
19×associate-/l*_binary64_2410
16×prod-exp_binary64_2514 cbrt-unprod_binary64_2498
13×associate-/r*_binary64_2409
distribute-lft-out_binary64_2416
unswap-sqr_binary64_2433 pow1_binary64_2526
associate-/l/_binary64_2412
add-log-exp_binary64_2504
associate-*r/_binary64_2407 clear-num_binary64_2464 frac-2neg_binary64_2476
flip--_binary64_2440 flip3--_binary64_2469
associate-*l/_binary64_2408 *-commutative_binary64_2396 frac-times_binary64_2475 pow-prod-down_binary64_2536
Counts
4 → 395
Calls

8 calls:

132.0ms
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
22.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
13.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
0.0ms
(*.f64 i (+.f64 i (+.f64 alpha beta)))

series9.1s (31.2%)

Counts
4 → 77
Calls

4 calls:

7.2s
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
1.5s
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
272.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
181.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
Compiler

Compiled 17611 to 12259 computations (30.4% saved)

simplify312.0ms (1.1%)

Algorithm
egg-herbie
Counts
472 → 472
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0524536962

prune1.8s (6.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4684472
Fresh235
Picked101
Done011
Total4718479
Error
8.1b
Counts
479 → 8
Compiler

Compiled 38379 to 16368 computations (57.4% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (*.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.0b
(*.f64 i (+.f64 i (+.f64 alpha beta)))
0.0b
(*.f64 i (+.f64 i (+.f64 alpha beta)))
0.0b
(*.f64 i (+.f64 i (+.f64 alpha beta)))
0.1b
(*.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
37.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
38.0b
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
38.0b
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))

rewrite69.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64_2487
25×times-frac_binary64_2471
24×associate-*r*_binary64_2405
23×*-un-lft-identity_binary64_2465 sqrt-prod_binary64_2481 add-cube-cbrt_binary64_2500
14×add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
pow1_binary64_2526 sqrt-div_binary64_2482
flip3-+_binary64_2468 flip-+_binary64_2439
unswap-sqr_binary64_2433 associate-*l*_binary64_2406
add-log-exp_binary64_2504 associate-/r/_binary64_2411
associate-/r*_binary64_2409 associate-*r/_binary64_2407 cbrt-undiv_binary64_2499 div-exp_binary64_2516 prod-exp_binary64_2514 cbrt-unprod_binary64_2498
associate-*l/_binary64_2408 frac-times_binary64_2475 pow1/2_binary64_2545 associate-/l/_binary64_2412 div-inv_binary64_2462 rem-sqrt-square_binary64_2478 sqrt-pow1_binary64_2483
*-commutative_binary64_2396 clear-num_binary64_2464 frac-2neg_binary64_2476 pow-prod-down_binary64_2536 associate-/l*_binary64_2410
Counts
4 → 109
Calls

8 calls:

25.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
13.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
0.0ms
(*.f64 i (+.f64 i (+.f64 alpha beta)))

series817.0ms (2.8%)

Counts
4 → 63
Calls

4 calls:

271.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
199.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
176.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
171.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
Compiler

Compiled 8023 to 4706 computations (41.3% saved)

simplify113.0ms (0.4%)

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049875108
149875108

prune391.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh066
Picked011
Done011
Total1728180
Error
8.1b
Counts
180 → 8
Compiler

Compiled 12601 to 4394 computations (65.1% saved)

simplify61.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
05124667
15124667

regimes539.0ms (1.8%)

Compiler

Compiled 9342 to 4863 computations (47.9% saved)

bsearch32.0ms (0.1%)

Steps
ItersRangePoint
7
1.7314361485825164e+121
2.882623618781556e+123
3.0038864540210744e+122
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes185.0ms (0.6%)

Compiler

Compiled 2139 to 1308 computations (38.8% saved)

bsearch29.0ms (0.1%)

Steps
ItersRangePoint
7
1.7314361485825164e+121
2.882623618781556e+123
7.983772415137889e+122
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes154.0ms (0.5%)

Compiler

Compiled 1662 to 1065 computations (35.9% saved)

bsearch29.0ms (0.1%)

Steps
ItersRangePoint
7
1.7314361485825164e+121
2.882623618781556e+123
1.4998886754282225e+123
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes140.0ms (0.5%)

Compiler

Compiled 1344 to 900 computations (33% saved)

bsearch31.0ms (0.1%)

Steps
ItersRangePoint
7
1.7314361485825164e+121
2.882623618781556e+123
1.882778091047329e+123
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes128.0ms (0.4%)

Compiler

Compiled 1185 to 819 computations (30.9% saved)

bsearch28.0ms (0.1%)

Steps
ItersRangePoint
7
1.7314361485825164e+121
2.882623618781556e+123
2.4188232729140788e+123
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes120.0ms (0.4%)

Compiler

Compiled 1044 to 732 computations (29.9% saved)

bsearch29.0ms (0.1%)

Steps
ItersRangePoint
8
2.0374507719293203e+130
2.9660913223250503e+133
4.086212311574064e+131
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes45.0ms (0.2%)

Compiler

Compiled 210 to 204 computations (2.9% saved)

bsearch0.0ms (0%)

regimes34.0ms (0.1%)

Accuracy

Total 3.3b remaining (29.9%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch37.0ms (0.1%)

Steps
ItersRangePoint
8
4.4264350272148485e+204
1.532220757773531e+208
4.483882443948973e+204
Compiler

Compiled 323 to 199 computations (38.4% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
083475
183475

end0.0ms (0%)

sample2.6s (9%)

Algorithm
intervals
Results
630.0ms8000×body128valid
184.0ms8000×pre128true
Compiler

Compiled 3497 to 1848 computations (47.2% saved)

Pareto

0.3761852493894276

Profiling

Loading profile data...