Details

Time bar (total: 3.6s)

analyze3.0ms

Algorithm
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

sample31.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
4.0ms256×pre80true

simplify192.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (189.0ms)

IterNodesCost
0498625
1498625

prune9.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.5b

Counts
2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
10.2b
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
11.3b
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity_binary64
34×distribute-lft-out_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
24×flip3-+_binary64 flip-+_binary64
21×associate-*r*_binary64 add-sqr-sqrt_binary64
18×associate-/r/_binary64
16×frac-times_binary64
15×add-cube-cbrt_binary64
14×times-frac_binary64
13×pow1_binary64
11×swap-sqr_binary64
10×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64 associate-*l/_binary64
9×associate-*l*_binary64
8×associate-*r/_binary64
7×associate-/l/_binary64
6×associate-/r*_binary64
5×associate-/l*_binary64
4×add-log-exp_binary64
3×unswap-sqr_binary64 div-inv_binary64
2×pow-prod-down_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
1×pow-prod-up_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 pow-plus_binary64 pow-sqr_binary64 pow2_binary64
Counts
4 → 158
Calls
4 calls:
15.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
27.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
26.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
27.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
29.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
14.0ms
(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

simplify48.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
053302658

prune217.0ms

Filtered
111 candidates to 170 candidates (-53.2%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1637170
Fresh101
Picked101
Done000
Total1657172

Merged error: 0.0b

Counts
172 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b
(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
10.2b
(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
826×*-un-lft-identity_binary64
508×times-frac_binary64
374×distribute-lft-out_binary64
191×add-sqr-sqrt_binary64
182×add-cube-cbrt_binary64
136×associate-*r*_binary64
34×add-exp-log_binary64 add-cbrt-cube_binary64
31×associate-/l*_binary64
30×associate-/r/_binary64
20×flip3-+_binary64 flip-+_binary64
15×associate-/r*_binary64 div-inv_binary64
14×cbrt-undiv_binary64 div-exp_binary64
8×associate-/l/_binary64
6×pow1_binary64 cbrt-unprod_binary64 prod-exp_binary64
4×add-log-exp_binary64 associate-*l*_binary64 frac-times_binary64 associate-*l/_binary64
3×unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64
2×associate-*r/_binary64
1×pow-prod-down_binary64 *-commutative_binary64
Counts
4 → 422
Calls
4 calls:
11.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
25.0ms
(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
34.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
50.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

series83.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
14.0ms
(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
35.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
26.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

simplify106.0ms

Algorithm
egg-herbie
Counts
434 → 434
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049638383
149638383

prune402.0ms

Filtered
186 candidates to 434 candidates (-133.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4295434
Fresh336
Picked101
Done000
Total4338441

Merged error: 0b

Counts
441 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2))
0.1b
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
0.1b
(*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
10.2b
(*.f64 (+.f64 alpha 1) (/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log_binary64
66×*-un-lft-identity_binary64
52×add-cbrt-cube_binary64
32×associate-*r*_binary64 times-frac_binary64
30×add-sqr-sqrt_binary64 div-exp_binary64
28×prod-exp_binary64
26×distribute-lft-out_binary64
21×add-cube-cbrt_binary64
18×cbrt-undiv_binary64
16×cbrt-unprod_binary64
12×flip3-+_binary64 flip-+_binary64
11×associate-/l/_binary64
10×associate-/r*_binary64
8×pow1_binary64 associate-/r/_binary64 associate-*l*_binary64 frac-times_binary64 associate-*l/_binary64
4×add-log-exp_binary64 1-exp_binary64 associate-*r/_binary64 unswap-sqr_binary64 rec-exp_binary64 div-inv_binary64
2×pow-prod-down_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 un-div-inv_binary64 *-commutative_binary64
Counts
4 → 166
Calls
4 calls:
19.0ms
(/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2))
31.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
16.0ms
(*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
24.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2))
30.0ms
(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.0ms
(*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
25.0ms
(*.f64 (+.f64 alpha 1) (/.f64 (*.f64 (+.f64 beta 1) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)))

simplify46.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050382836

prune181.0ms

Filtered
111 candidates to 178 candidates (-60.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1780178
Fresh077
Picked011
Done000
Total1788186

Merged error: 0b

Counts
186 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b
(/.f64 (*.f64 (sqrt.f64 (+.f64 alpha 1)) (*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
5.1b
(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
5.1b
(*.f64 (sqrt.f64 (+.f64 alpha 1)) (*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
783×*-un-lft-identity_binary64
491×times-frac_binary64
354×distribute-lft-out_binary64
192×add-sqr-sqrt_binary64
174×add-cube-cbrt_binary64
143×associate-*l*_binary64
52×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
40×flip3-+_binary64 flip-+_binary64
34×frac-times_binary64
28×associate-/r/_binary64
27×associate-/l*_binary64
24×associate-*r/_binary64
18×associate-/l/_binary64
17×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
14×div-inv_binary64
11×pow1_binary64 sqrt-prod_binary64 associate-*l/_binary64
10×associate-/r*_binary64
8×associate-*r*_binary64
6×unswap-sqr_binary64
4×pow-prod-down_binary64 add-log-exp_binary64
2×clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 440
Calls
4 calls:
20.0ms
(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
45.0ms
(/.f64 (*.f64 (sqrt.f64 (+.f64 alpha 1)) (*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
63.0ms
(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
40.0ms
(*.f64 (sqrt.f64 (+.f64 alpha 1)) (*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))

series102.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
27.0ms
(/.f64 (*.f64 (sqrt.f64 (+.f64 alpha 1)) (*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
27.0ms
(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
32.0ms
(*.f64 (sqrt.f64 (+.f64 alpha 1)) (*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))

simplify124.0ms

Algorithm
egg-herbie
Counts
452 → 452
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0494010025
1494010025

prune455.0ms

Filtered
203 candidates to 452 candidates (-122.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4511452
Fresh156
Picked011
Done011
Total4528460

Merged error: 0b

Counts
460 → 8

regimes102.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02527
12527

end0.0ms

sample769.0ms

Algorithm
intervals
Results
490.0ms8000×body80valid
130.0ms8000×pre80true

Profiling

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