Details

Time bar (total: 38.7s)

analyze2.4s (6.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%98.2%1.8%7
0%92%8%8
0%91.2%8.8%9
0.4%89.3%10.3%10
7.1%79.2%13.6%11
11.9%70.2%17.9%12
13.8%67.4%18.7%13
16.6%63.3%20.1%14
Compiler

Compiled 41 to 33 computations (19.5% saved)

sample138.0ms (0.4%)

Algorithm
intervals
Results
25.0ms180×body128valid
21.0ms41×body1024nan
16.0ms18×body2048valid
13.0ms23×body1024valid
12.0ms17×body2048nan
11.0ms78×body128nan
8.0ms21×body512valid
7.0ms17×body512nan
4.0ms14×body256valid
3.0ms11×body256nan
Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify139.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0539061

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 48.4b

Counts
2 → 1
Compiler

Compiled 80 to 59 computations (26.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.1b
(*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)
12.9b
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
18.9b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite100.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
66×sqrt-div_binary64_2482
40×associate-*r/_binary64_2407
39×*-un-lft-identity_binary64_2465
36×times-frac_binary64_2471
35×add-sqr-sqrt_binary64_2487
34×associate-*l/_binary64_2408
32×add-cube-cbrt_binary64_2500
25×flip3-+_binary64_2468 flip-+_binary64_2439
24×frac-times_binary64_2475 frac-sub_binary64_2474
22×flip--_binary64_2440 flip3--_binary64_2469
20×associate-/l/_binary64_2412 distribute-neg-frac_binary64_2429
17×pow1_binary64_2526
16×distribute-lft-neg-in_binary64_2422 distribute-rgt-neg-in_binary64_2423
15×sqrt-prod_binary64_2481
12×associate-/l*_binary64_2410
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
pow-prod-down_binary64_2536
sqrt-pow1_binary64_2483
add-log-exp_binary64_2504 unpow-prod-down_binary64_2544 neg-mul-1_binary64_2461
associate-/r*_binary64_2409 associate-*r*_binary64_2405 distribute-lft-out_binary64_2416 associate-*l*_binary64_2406
pow1/2_binary64_2545 associate-/r/_binary64_2411
*-commutative_binary64_2396 clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-sub_binary64_2470 distribute-lft-out--_binary64_2417 unswap-sqr_binary64_2433 div-exp_binary64_2516 div-inv_binary64_2462 rem-sqrt-square_binary64_2478 prod-exp_binary64_2514 frac-2neg_binary64_2476 distribute-frac-neg_binary64_2428 neg-sub0_binary64_2460 cbrt-unprod_binary64_2498
Counts
4 → 158
Calls

4 calls:

27.0ms
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
21.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
11.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
8.0ms
(*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)

series860.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

370.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
363.0ms
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
70.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
57.0ms
(*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)

simplify145.0ms (0.4%)

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
0494811070
1494811070

prune626.0ms (1.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New15416170
Fresh000
Picked101
Done000
Total15516171

Merged error: 43.2b

Counts
171 → 16
Compiler

Compiled 12068 to 6839 computations (43.3% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

14.8b
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))
20.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite152.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
404×sqrt-div_binary64_2482
136×associate-*r/_binary64_2407
122×flip3-+_binary64_2468 flip-+_binary64_2439
120×frac-times_binary64_2475
104×associate-*l/_binary64_2408
96×frac-sub_binary64_2474
56×associate-/l/_binary64_2412 distribute-neg-frac_binary64_2429
45×flip--_binary64_2440 flip3--_binary64_2469
36×times-frac_binary64_2471
33×add-sqr-sqrt_binary64_2487
31×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500
16×distribute-lft-neg-in_binary64_2422 distribute-rgt-neg-in_binary64_2423 pow1_binary64_2526
15×sqrt-prod_binary64_2481
12×associate-/l*_binary64_2410
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
add-log-exp_binary64_2504 neg-mul-1_binary64_2461
associate-/r*_binary64_2409 pow1/2_binary64_2545
rem-sqrt-square_binary64_2478 associate-/r/_binary64_2411
clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-sub_binary64_2470 div-exp_binary64_2516 div-inv_binary64_2462 frac-2neg_binary64_2476 distribute-frac-neg_binary64_2428 neg-sub0_binary64_2460
Counts
4 → 222
Calls

4 calls:

30.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
22.0ms
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series864.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

376.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
364.0ms
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))
63.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
62.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify197.0ms (0.5%)

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0555820240

prune1.4s (3.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New22410234
Fresh31215
Picked101
Done000
Total22822250

Merged error: 43.2b

Counts
250 → 22
Compiler

Compiled 23726 to 12675 computations (46.6% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

20.4b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.5b
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.5b
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite110.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
202×sqrt-div_binary64_2482
104×associate-*r/_binary64_2407
63×flip3-+_binary64_2468 flip-+_binary64_2439
60×frac-times_binary64_2475
56×associate-/l/_binary64_2412 distribute-neg-frac_binary64_2429
52×associate-*l/_binary64_2408
48×frac-sub_binary64_2474
40×cbrt-div_binary64_2497
36×times-frac_binary64_2471
33×add-sqr-sqrt_binary64_2487
32×*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500
23×flip--_binary64_2440 flip3--_binary64_2469
16×distribute-lft-neg-in_binary64_2422 distribute-rgt-neg-in_binary64_2423
12×associate-/l*_binary64_2410
11×sqrt-prod_binary64_2481
add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 cbrt-prod_binary64_2496
pow1_binary64_2526
add-log-exp_binary64_2504 neg-mul-1_binary64_2461
associate-/r*_binary64_2409
pow1/3_binary64_2547 associate-/r/_binary64_2411
pow1/2_binary64_2545 clear-num_binary64_2464 cbrt-undiv_binary64_2499 div-sub_binary64_2470 div-exp_binary64_2516 div-inv_binary64_2462 rem-sqrt-square_binary64_2478 frac-2neg_binary64_2476 sqrt-pow1_binary64_2483 distribute-frac-neg_binary64_2428 neg-sub0_binary64_2460
Counts
4 → 164
Calls

4 calls:

33.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series19.1s (49.5%)

Counts
4 → 12
Calls

4 calls:

18.8s
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
157.0ms
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
145.0ms
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
60.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify156.0ms (0.4%)

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0495816721
1495816721

prune1.3s (3.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New1679176
Fresh81321
Picked101
Done000
Total17622198

Merged error: 43.2b

Counts
198 → 22
Compiler

Compiled 22714 to 12202 computations (46.3% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
32.3b
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.5b
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite43.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64_2487
sqrt-prod_binary64_2481
*-un-lft-identity_binary64_2465 add-cube-cbrt_binary64_2500
pow1_binary64_2526
sqrt-div_binary64_2482
flip3-+_binary64_2468 add-log-exp_binary64_2504 flip-+_binary64_2439 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501
pow1/2_binary64_2545 rem-sqrt-square_binary64_2478 sqrt-pow1_binary64_2483 cbrt-prod_binary64_2496
cbrt-div_binary64_2497
pow1/3_binary64_2547
Counts
4 → 58
Calls

4 calls:

8.0ms
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series376.0ms (1%)

Counts
4 → 12
Calls

4 calls:

166.0ms
(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
73.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
70.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
67.0ms
(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify60.0ms (0.2%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049591280
149591280

prune265.0ms (0.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New68270
Fresh21921
Picked101
Done000
Total712192

Merged error: 43.2b

Counts
92 → 21
Compiler

Compiled 5916 to 3411 computations (42.3% saved)

regimes2.0s (5.2%)

Compiler

Compiled 37251 to 23717 computations (36.3% saved)

bsearch111.0ms (0.3%)

Steps
ItersRangePoint
9
-8.70139126693451e+29
-1.0689577505403694e+24
-8.580045937962391e+29
Compiler

Compiled 1 to 4 computations (-300% saved)

simplify23.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0565180
1565180

end0.0ms (0%)

sample8.0s (20.7%)

Algorithm
intervals
Results
781.0ms5526×body128valid
513.0ms693×body2048valid
488.0ms867×body1024nan
453.0ms816×body1024valid
447.0ms634×body2048nan
346.0ms2489×body128nan
267.0ms613×body512valid
221.0ms548×body512nan
95.0ms350×body256valid
78.0ms303×body256nan
1.0msbody4096valid
Compiler

Compiled 6328 to 4027 computations (36.4% saved)

Profiling

Loading profile data...