Details

Time bar (total: 27.4s)

analyze127.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.1%)

Algorithm
intervals
Results
11.0ms205×body128valid
6.0ms25×body1024valid
6.0ms256×pre128true
2.0ms15×body512valid
1.0msbody256valid
1.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify163.0ms (0.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
0537143

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
23.0b
Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.5b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
20.3b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite323.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
12.7b
Rules
54×times-frac_binary64_2471
47×*-un-lft-identity_binary64_2465
25×add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
17×add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
14×associate-/r/_binary64_2411
11×flip3-+_binary64_2468 flip-+_binary64_2439 distribute-lft-out_binary64_2416
10×associate-/l*_binary64_2410
associate-/l/_binary64_2412
div-exp_binary64_2516 cbrt-undiv_binary64_2499 div-inv_binary64_2462 associate-/r*_binary64_2409
add-log-exp_binary64_2504
frac-times_binary64_2475
pow1_binary64_2526 flip3--_binary64_2469 flip--_binary64_2440
prod-exp_binary64_2514 cbrt-unprod_binary64_2498 frac-2neg_binary64_2476 clear-num_binary64_2464 associate-*l/_binary64_2408 associate-*r/_binary64_2407
sum-log_binary64_2556 +-commutative_binary64_2395
Counts
3 → 111
Calls

3 calls:

33.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
24.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
14.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 5370 to 2710 computations (49.5% saved)

series3.5s (12.6%)

Error
0.4b
Counts
3 → 74
Calls

3 calls:

1.8s
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.2s
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
213.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 14539 to 11194 computations (23% saved)

simplify108.0ms (0.4%)

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0504811951

prune554.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1769185
Fresh000
Picked101
Done000
Total1779186
Error
0.1b
Counts
186 → 9
Compiler

Compiled 10475 to 5752 computations (45.1% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
1.1b
(*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
3.0b
(+.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)

rewrite869.0ms (3.2%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
321×times-frac_binary64_2471
290×*-un-lft-identity_binary64_2465
211×add-sqr-sqrt_binary64_2487
140×add-cube-cbrt_binary64_2500
90×associate-*r*_binary64_2405
44×distribute-lft-out_binary64_2416
31×difference-of-squares_binary64_2434 distribute-lft-out--_binary64_2417
26×associate-/l*_binary64_2410
24×associate-/r/_binary64_2411
20×add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
15×flip3-+_binary64_2468 flip-+_binary64_2439
12×div-inv_binary64_2462
div-exp_binary64_2516 cbrt-undiv_binary64_2499 associate-/r*_binary64_2409
add-log-exp_binary64_2504 pow1_binary64_2526
associate-*l*_binary64_2406
prod-exp_binary64_2514 cbrt-unprod_binary64_2498 unswap-sqr_binary64_2433 div-sub_binary64_2470 associate-/l/_binary64_2412
frac-times_binary64_2475 associate-*l/_binary64_2408 frac-2neg_binary64_2476 clear-num_binary64_2464
sum-log_binary64_2556 +-commutative_binary64_2395 pow-prod-down_binary64_2536 associate-*r/_binary64_2407 *-commutative_binary64_2396 flip3--_binary64_2469 flip--_binary64_2440
Counts
4 → 295
Calls

4 calls:

43.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
27.0ms
(+.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
20.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
11.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 14908 to 7929 computations (46.8% saved)

series4.5s (16.5%)

Error
0.1b
Counts
4 → 101
Calls

4 calls:

1.8s
(+.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
1.2s
(*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
876.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))
219.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 19962 to 15184 computations (23.9% saved)

simplify234.0ms (0.9%)

Algorithm
egg-herbie
Counts
396 → 396
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
0497722369
1497722369

prune1.3s (4.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3942396
Fresh358
Picked011
Done000
Total3978405
Error
0.1b
Counts
405 → 8
Compiler

Compiled 21444 to 11677 computations (45.5% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 (+.f64 beta alpha) (/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta)))) 1)
0.0b
(*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta))
2.2b
(*.f64 (+.f64 beta alpha) (/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta))))
9.1b
(/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta)))

rewrite262.0ms (1%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
21×flip3-+_binary64_2468 flip-+_binary64_2439
20×add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
18×associate-*r*_binary64_2405
16×associate-/r/_binary64_2411
15×add-sqr-sqrt_binary64_2487
14×frac-times_binary64_2475
13×*-un-lft-identity_binary64_2465
11×add-cube-cbrt_binary64_2500
pow1_binary64_2526 associate-*l/_binary64_2408
associate-*r/_binary64_2407 associate-*l*_binary64_2406
prod-exp_binary64_2514 add-log-exp_binary64_2504 cbrt-unprod_binary64_2498 times-frac_binary64_2471
div-exp_binary64_2516 cbrt-undiv_binary64_2499
associate-/l*_binary64_2410
div-inv_binary64_2462 pow-prod-down_binary64_2536 unswap-sqr_binary64_2433 *-commutative_binary64_2396
frac-2neg_binary64_2476 clear-num_binary64_2464 associate-/r*_binary64_2409 distribute-lft-out_binary64_2416 distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414 sum-log_binary64_2556 +-commutative_binary64_2395
Counts
4 → 108
Calls

4 calls:

19.0ms
(*.f64 (+.f64 beta alpha) (/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta))))
17.0ms
(+.f64 (*.f64 (+.f64 beta alpha) (/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta)))) 1)
15.0ms
(/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta)))
12.0ms
(*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta))
Compiler

Compiled 4248 to 2824 computations (33.5% saved)

series1.3s (4.6%)

Error
0.1b
Counts
4 → 72
Calls

4 calls:

427.0ms
(+.f64 (*.f64 (+.f64 beta alpha) (/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta)))) 1)
401.0ms
(*.f64 (+.f64 beta alpha) (/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta))))
176.0ms
(*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta))
150.0ms
(/.f64 beta (*.f64 (+.f64 (*.f64 2 i) (+.f64 2 beta)) (+.f64 (*.f64 2 i) beta)))
Compiler

Compiled 6818 to 5324 computations (21.9% saved)

simplify91.0ms (0.3%)

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049986284
149986284

prune314.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1791180
Fresh156
Picked011
Done011
Total1808188
Error
0.1b
Counts
188 → 8
Compiler

Compiled 6735 to 4280 computations (36.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

19.0b
(/.f64 (*.f64 (/.f64 (pow.f64 (+.f64 beta alpha) 2) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (/.f64 (*.f64 (-.f64 beta alpha) (-.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (*.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
20.3b
(/.f64 (*.f64 (-.f64 beta alpha) (-.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
20.3b
(/.f64 (*.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
20.3b
(/.f64 (pow.f64 (+.f64 beta alpha) 2) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

rewrite1.1s (4%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
144×add-exp-log_binary64_2503
81×add-cbrt-cube_binary64_2501
67×div-exp_binary64_2516
47×prod-exp_binary64_2514
34×times-frac_binary64_2471 *-un-lft-identity_binary64_2465
33×cbrt-undiv_binary64_2499
26×add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
25×cbrt-unprod_binary64_2498
19×associate-/l/_binary64_2412
16×unpow-prod-down_binary64_2544
14×associate-/r/_binary64_2411
13×frac-times_binary64_2475
12×flip3-+_binary64_2468 flip-+_binary64_2439 associate-/l*_binary64_2410
10×associate-/r*_binary64_2409
flip3--_binary64_2469 flip--_binary64_2440
pow-to-exp_binary64_2534 pow-exp_binary64_2533 associate-*l/_binary64_2408 associate-*r/_binary64_2407
pow1_binary64_2526 add-log-exp_binary64_2504 frac-2neg_binary64_2476 distribute-lft-out_binary64_2416 unpow2_binary64_2530 sqr-pow_binary64_2437 clear-num_binary64_2464 div-inv_binary64_2462
Counts
4 → 181
Calls

4 calls:

45.0ms
(/.f64 (*.f64 (/.f64 (pow.f64 (+.f64 beta alpha) 2) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (/.f64 (*.f64 (-.f64 beta alpha) (-.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (*.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
15.0ms
(/.f64 (*.f64 (-.f64 beta alpha) (-.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
14.0ms
(/.f64 (*.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
12.0ms
(/.f64 (pow.f64 (+.f64 beta alpha) 2) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 18418 to 9200 computations (50% saved)

series4.1s (14.9%)

Error
0.1b
Counts
4 → 81
Calls

4 calls:

3.0s
(/.f64 (*.f64 (/.f64 (pow.f64 (+.f64 beta alpha) 2) (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (/.f64 (*.f64 (-.f64 beta alpha) (-.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))) (*.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
257.0ms
(/.f64 (*.f64 (-.f64 beta alpha) (-.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
255.0ms
(/.f64 (*.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
211.0ms
(/.f64 (pow.f64 (+.f64 beta alpha) 2) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
Compiler

Compiled 22349 to 14783 computations (33.9% saved)

simplify133.0ms (0.5%)

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0495712135
1495712135

prune1.3s (4.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2611262
Fresh055
Picked101
Done022
Total2628270
Error
0.1b
Counts
270 → 8
Compiler

Compiled 23701 to 12458 computations (47.4% saved)

regimes2.3s (8.3%)

Accuracy

Total 1.5b remaining (98%)

Threshold costs 0b (0%)

Compiler

Compiled 39655 to 27070 computations (31.7% saved)

bsearch9.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0270185
1270185

end0.0ms (0%)

sample4.7s (17.3%)

Algorithm
intervals
Results
367.0ms6439×body128valid
178.0ms8000×pre128true
163.0ms712×body1024valid
90.0ms507×body512valid
32.0ms288×body256valid
22.0ms54×body2048valid
Compiler

Compiled 5718 to 3888 computations (32% saved)

Profiling

Loading profile data...