Details

Time bar (total: 2.5min)

analyze3.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
42.1%14%43.8%3
42.1%14%43.8%4
52.7%3.5%43.8%5
56.2%0%43.8%6

sample27.0ms (0%)

Algorithm
1×intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify144.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (141.0ms)

IterNodesCost
0494935
1494935

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 3.9b

Counts
2 → 1

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0)
0.0b
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
0.1b
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
3.6b
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))

rewrite125.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
804×times-frac_binary64
586×*-un-lft-identity_binary64
340×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
123×distribute-lft-out_binary64
82×associate-/l*_binary64
54×associate-/r/_binary64
29×flip3-+_binary64 flip-+_binary64
27×div-inv_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
13×add-log-exp_binary64
10×associate-/r*_binary64 cbrt-undiv_binary64 div-exp_binary64
6×sum-log_binary64
4×associate-/l/_binary64 pow1_binary64
3×clear-num_binary64 frac-2neg_binary64
1×associate-+l+_binary64 +-commutative_binary64
Counts
4 → 465
Calls

4 calls:

39.0ms
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
22.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
19.0ms
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
9.0ms
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0)

series78.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

31.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
29.0ms
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
15.0ms
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
3.0ms
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0)

simplify158.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0497323485
1497323485

prune2.0s (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New46710477
Fresh000
Picked101
Done000
Total46810478

Merged error: 1.4b

Counts
478 → 10

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
0.0b
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
0.1b
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (+.f64 1.0 (*.f64 1.0 2.0))))
3.6b
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))

rewrite130.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
954×times-frac_binary64
828×*-un-lft-identity_binary64
383×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
253×distribute-lft-out_binary64
82×associate-/l*_binary64
66×associate-/r/_binary64
37×flip3-+_binary64 flip-+_binary64
31×div-inv_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
11×associate-/r*_binary64
10×cbrt-undiv_binary64 div-exp_binary64
9×add-log-exp_binary64
4×associate-/l/_binary64 pow1_binary64 frac-add_binary64
3×clear-num_binary64 frac-2neg_binary64 sum-log_binary64
1×associate-+l+_binary64 +-commutative_binary64
Counts
4 → 528
Calls

4 calls:

40.0ms
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (+.f64 1.0 (*.f64 1.0 2.0))))
22.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
18.0ms
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
6.0ms
(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))

series81.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

34.0ms
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (+.f64 1.0 (*.f64 1.0 2.0))))
27.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
15.0ms
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
5.0ms
(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))

simplify164.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
540 → 540
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0560027238

prune2.8s (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New5400540
Fresh099
Picked011
Done000
Total54010550

Merged error: 1.4b

Counts
550 → 10

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
0.1b
(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
0.7b
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))))
3.4b
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0))))

rewrite1.0s (0.7%)

Algorithm
1×rewrite-expression-head
Rules
12132×times-frac_binary64
7340×*-un-lft-identity_binary64
4744×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
3270×sqrt-prod_binary64
1298×distribute-lft-out_binary64
784×associate-/l*_binary64
298×associate-/r/_binary64
284×sqrt-div_binary64
150×flip3-+_binary64 flip-+_binary64
149×div-inv_binary64
34×add-exp-log_binary64 add-cbrt-cube_binary64
20×cbrt-undiv_binary64 div-exp_binary64
19×associate-/r*_binary64
5×associate-/l/_binary64
4×add-log-exp_binary64 pow1_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 3894
Calls

4 calls:

162.0ms
(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
65.0ms
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
29.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))))
17.0ms
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0))))

series97.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

36.0ms
(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
28.0ms
(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
17.0ms
(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0))))
16.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))))

simplify1.4s (1%)

Algorithm
1×egg-herbie
Counts
3906 → 3906
Iterations

Useful iterations: 0 (108.0ms)

IterNodesCost
05589286573

prune2.4min (94.5%)

Profiling

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