Details

Time bar (total: 19.4s)

analyze125.0ms (0.6%)

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)

sample39.0ms (0.2%)

Algorithm
intervals
Results
12.0ms209×body128valid
6.0ms256×pre128true
4.0ms18×body1024valid
3.0ms16×body512valid
1.0ms11×body256valid
1.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify268.0ms (1.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
0489443
1489443

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 21.6b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0.1%)

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))
1.4b
(+.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)
18.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite96.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64_2493
47×*-un-lft-identity_binary64_2487
25×add-cube-cbrt_binary64_2522 add-sqr-sqrt_binary64_2509
17×add-exp-log_binary64_2525 add-cbrt-cube_binary64_2523
14×associate-/r/_binary64_2433
11×distribute-lft-out_binary64_2438 flip-+_binary64_2461 flip3-+_binary64_2490
10×associate-/l*_binary64_2432
associate-/l/_binary64_2434
associate-/r*_binary64_2431 div-inv_binary64_2484 div-exp_binary64_2538 cbrt-undiv_binary64_2521
add-log-exp_binary64_2526
frac-times_binary64_2497
flip--_binary64_2462 pow1_binary64_2548 flip3--_binary64_2491
associate-*l/_binary64_2430 prod-exp_binary64_2536 frac-2neg_binary64_2498 clear-num_binary64_2486 cbrt-unprod_binary64_2520 associate-*r/_binary64_2429
+-commutative_binary64_2417 sum-log_binary64_2578
Counts
3 → 111
Calls

3 calls:

37.0ms
(+.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)
27.0ms
(/.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))
16.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (7.2%)

Counts
3 → 9
Calls

3 calls:

689.0ms
(+.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)
590.0ms
(/.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))
125.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify102.0ms (0.5%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049355261
149355261

prune974.0ms (5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10911120
Fresh000
Picked101
Done000
Total11011121

Merged error: 7.0b

Counts
121 → 11
Compiler

Compiled 25615 to 15456 computations (39.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.5b
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite326.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
603×times-frac_binary64_2493
484×*-un-lft-identity_binary64_2487
408×add-sqr-sqrt_binary64_2509
260×add-cube-cbrt_binary64_2522
219×sqrt-prod_binary64_2503
153×associate-*r*_binary64_2427
67×distribute-lft-out_binary64_2438
45×difference-of-squares_binary64_2456 distribute-lft-out--_binary64_2439
38×associate-/r/_binary64_2433
34×associate-*l*_binary64_2428
32×add-exp-log_binary64_2525 add-cbrt-cube_binary64_2523
25×associate-/l*_binary64_2432
21×flip-+_binary64_2461 flip3-+_binary64_2490
19×div-inv_binary64_2484
15×unswap-sqr_binary64_2455
14×associate-/r*_binary64_2431
13×div-exp_binary64_2538 cbrt-undiv_binary64_2521
sqrt-div_binary64_2504
prod-exp_binary64_2536 cbrt-unprod_binary64_2520 pow1_binary64_2548 add-log-exp_binary64_2526
associate-/l/_binary64_2434
frac-2neg_binary64_2498 clear-num_binary64_2486 div-sub_binary64_2492
associate-*l/_binary64_2430 *-commutative_binary64_2418 frac-times_binary64_2497 +-commutative_binary64_2417 sum-log_binary64_2578 pow-prod-down_binary64_2558 associate-*r/_binary64_2429
Counts
4 → 485
Calls

4 calls:

131.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
43.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
27.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
13.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series2.0s (10.3%)

Counts
4 → 12
Calls

4 calls:

703.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
619.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
393.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
289.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify247.0ms (1.3%)

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0540027691

prune2.6s (13.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New4925497
Fresh3710
Picked011
Done000
Total49513508

Merged error: 7.0b

Counts
508 → 13
Compiler

Compiled 42112 to 24788 computations (41.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.8b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.8b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite174.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
321×times-frac_binary64_2493
290×*-un-lft-identity_binary64_2487
211×add-sqr-sqrt_binary64_2509
140×add-cube-cbrt_binary64_2522
90×associate-*r*_binary64_2427
44×distribute-lft-out_binary64_2438
31×difference-of-squares_binary64_2456 distribute-lft-out--_binary64_2439
26×associate-/l*_binary64_2432
24×associate-/r/_binary64_2433
20×add-exp-log_binary64_2525 add-cbrt-cube_binary64_2523
15×flip-+_binary64_2461 flip3-+_binary64_2490
12×div-inv_binary64_2484
associate-/r*_binary64_2431 div-exp_binary64_2538 cbrt-undiv_binary64_2521
pow1_binary64_2548 add-log-exp_binary64_2526
associate-*l*_binary64_2428
unswap-sqr_binary64_2455 prod-exp_binary64_2536 div-sub_binary64_2492 cbrt-unprod_binary64_2520 associate-/l/_binary64_2434
associate-*l/_binary64_2430 frac-2neg_binary64_2498 frac-times_binary64_2497 clear-num_binary64_2486
flip--_binary64_2462 *-commutative_binary64_2418 +-commutative_binary64_2417 sum-log_binary64_2578 pow-prod-down_binary64_2558 associate-*r/_binary64_2429 flip3--_binary64_2491
Counts
4 → 295
Calls

4 calls:

49.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
35.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
27.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
12.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (8.6%)

Counts
4 → 12
Calls

4 calls:

676.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
577.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
300.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
121.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify155.0ms (0.8%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0496913438
1496913438

prune910.0ms (4.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New3034307
Fresh2911
Picked011
Done011
Total30515320

Merged error: 7.0b

Counts
320 → 15
Compiler

Compiled 20488 to 11580 computations (43.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.8b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.8b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.9b
(log.f64 (exp.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))

rewrite190.0ms (1%)

Algorithm
rewrite-expression-head
Rules
306×times-frac_binary64_2493
274×*-un-lft-identity_binary64_2487
195×add-sqr-sqrt_binary64_2509
132×add-cube-cbrt_binary64_2522
90×associate-*r*_binary64_2427
44×distribute-lft-out_binary64_2438
27×difference-of-squares_binary64_2456 distribute-lft-out--_binary64_2439
22×associate-/r/_binary64_2433
21×associate-/l*_binary64_2432
18×add-exp-log_binary64_2525 add-cbrt-cube_binary64_2523
14×flip-+_binary64_2461 flip3-+_binary64_2490
11×div-inv_binary64_2484
pow1_binary64_2548
div-exp_binary64_2538 add-log-exp_binary64_2526 cbrt-undiv_binary64_2521
associate-/r*_binary64_2431 log-prod_binary64_2573 associate-*l*_binary64_2428 log-pow_binary64_2576
unswap-sqr_binary64_2455 prod-exp_binary64_2536 exp-prod_binary64_2539 cbrt-unprod_binary64_2520
associate-*l/_binary64_2430 frac-times_binary64_2497 div-sub_binary64_2492
*-commutative_binary64_2418 frac-2neg_binary64_2498 rem-log-exp_binary64_2528 clear-num_binary64_2486 +-commutative_binary64_2417 sum-log_binary64_2578 pow-prod-down_binary64_2558 exp-sum_binary64_2533 associate-/l/_binary64_2434 associate-*r/_binary64_2429
Counts
4 → 271
Calls

4 calls:

51.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
31.0ms
(log.f64 (exp.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))
30.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
22.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series2.7s (13.9%)

Counts
4 → 12
Calls

4 calls:

1.2s
(log.f64 (exp.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))
663.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
563.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
311.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify182.0ms (0.9%)

Algorithm
egg-herbie
Counts
283 → 283
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
0495013204
1495013204

prune736.0ms (3.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New2821283
Fresh11112
Picked011
Done022
Total28315298

Merged error: 7.0b

Counts
298 → 15
Compiler

Compiled 14683 to 8083 computations (44.9% saved)

regimes1.4s (7.4%)

Compiler

Compiled 22593 to 14650 computations (35.2% saved)

bsearch8.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
066110
166110

end0.0ms (0%)

sample3.0s (15.2%)

Algorithm
intervals
Results
387.0ms6479×body128valid
193.0ms8000×pre128true
155.0ms657×body1024valid
92.0ms498×body512valid
35.0ms308×body256valid
19.0ms58×body2048valid
Compiler

Compiled 3278 to 2123 computations (35.2% saved)

Profiling

Loading profile data...