Details

Time bar (total: 27.7s)

analyze48.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14

sample34.0ms

Algorithm
intervals
Results
19.0ms256×body128valid
5.0ms256×pre128true

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0539479

prune4.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 52.7b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
36.7b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
45.0b
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
86×times-frac_binary64
66×flip3-+_binary64 associate-/r/_binary64 flip-+_binary64
61×add-exp-log_binary64 add-cbrt-cube_binary64
46×add-sqr-sqrt_binary64
44×*-un-lft-identity_binary64 frac-times_binary64
34×associate-*r/_binary64
30×add-cube-cbrt_binary64
28×difference-of-squares_binary64
22×cbrt-unprod_binary64 prod-exp_binary64 associate-*l/_binary64
19×cbrt-undiv_binary64 div-exp_binary64
16×pow1_binary64
14×difference-of-sqr-1_binary64 associate-/l*_binary64
associate-/l/_binary64 div-inv_binary64
associate-/r*_binary64
associate-*r*_binary64
pow-prod-down_binary64 add-log-exp_binary64 associate-*l*_binary64
swap-sqr_binary64
distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
flip3--_binary64 pow-prod-up_binary64 pow-plus_binary64 unswap-sqr_binary64 pow-sqr_binary64 flip--_binary64 pow2_binary64
Counts
4 → 228
Calls
4 calls:
14.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
14.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
44.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
30.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series3.5s

Counts
4 → 12
Calls
4 calls:
102.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
206.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
2.9s
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
387.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify152.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0523418186

prune435.0ms

Filtered
152 candidates to 240 candidates (-57.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2346240
Fresh000
Picked101
Done000
Total2356241

Merged error: 33.9b

Counts
241 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.1b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
33.9b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
34.6b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
414×times-frac_binary64
314×add-sqr-sqrt_binary64
280×*-un-lft-identity_binary64
169×add-cube-cbrt_binary64
111×associate-*r*_binary64
70×add-exp-log_binary64 add-cbrt-cube_binary64
62×difference-of-squares_binary64
48×associate-/r/_binary64
42×associate-*l*_binary64
33×cbrt-undiv_binary64 div-exp_binary64
31×difference-of-sqr-1_binary64 distribute-lft-out--_binary64
24×flip3-+_binary64 div-inv_binary64 flip-+_binary64
19×associate-/l*_binary64
16×cbrt-unprod_binary64 prod-exp_binary64
13×associate-/r*_binary64
distribute-lft-out_binary64
pow1_binary64 unswap-sqr_binary64
associate-/l/_binary64
add-log-exp_binary64
associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64
flip3--_binary64 flip--_binary64
pow-prod-down_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 395
Calls
4 calls:
23.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
122.0ms
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
14.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series3.8s

Counts
4 → 12
Calls
4 calls:
382.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
3.1s
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
127.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
219.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify235.0ms

Algorithm
egg-herbie
Counts
407 → 407
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0515730002

prune843.0ms

Filtered
265 candidates to 407 candidates (-53.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4007407
Fresh235
Picked101
Done000
Total40310413

Merged error: 33.8b

Counts
413 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

4.4b
(/.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) 1) (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))))
33.9b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
34.5b
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
34.5b
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
13703×times-frac_binary64
7148×add-sqr-sqrt_binary64
6594×*-un-lft-identity_binary64
4938×add-cube-cbrt_binary64
3021×sqrt-prod_binary64
1104×difference-of-squares_binary64
552×difference-of-sqr-1_binary64 distribute-lft-out--_binary64
360×div-inv_binary64
348×associate-/r/_binary64
176×associate-/r*_binary64
165×flip3-+_binary64 flip-+_binary64
30×add-exp-log_binary64 add-cbrt-cube_binary64
23×associate-/l*_binary64
17×cbrt-undiv_binary64 div-exp_binary64
pow1_binary64
add-log-exp_binary64 sqrt-div_binary64
associate-/l/_binary64
pow1/2_binary64 associate-*r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64
cbrt-unprod_binary64 prod-exp_binary64
Counts
4 → 4080
Calls
4 calls:
138.0ms
(/.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) 1) (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))))
14.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))

series722.0ms

Counts
4 → 12
Calls
4 calls:
371.0ms
(/.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) 1) (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1) (/.f64 (sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))))
117.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
128.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
106.0ms
(sqrt.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))

simplify4.3s

Algorithm
egg-herbie
Counts
4092 → 4092
Iterations

Useful iterations: 0 (285.0ms)

IterNodesCost
04992532997
14992532997

prune4.9s

Filtered
822 candidates to 4092 candidates (-397.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New409204092
Fresh099
Picked011
Done000
Total4092104102

Merged error: 33.8b

Counts
4102 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
0.1b
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
33.9b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
34.6b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
190×times-frac_binary64
152×add-sqr-sqrt_binary64
132×*-un-lft-identity_binary64
111×associate-*r*_binary64
94×add-exp-log_binary64 add-cbrt-cube_binary64
83×add-cube-cbrt_binary64
43×cbrt-undiv_binary64 div-exp_binary64
30×difference-of-squares_binary64
25×cbrt-unprod_binary64 prod-exp_binary64
24×associate-/r/_binary64
15×difference-of-sqr-1_binary64 distribute-lft-out--_binary64
13×flip3-+_binary64 flip-+_binary64
12×div-inv_binary64
10×associate-/r*_binary64
associate-*l*_binary64
associate-/l/_binary64
pow1_binary64
associate-/l*_binary64
add-log-exp_binary64 associate-*r/_binary64
unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64
distribute-lft-out_binary64 frac-times_binary64 associate-*l/_binary64
pow-prod-down_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64
Counts
4 → 253
Calls
4 calls:
67.0ms
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
52.0ms
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
14.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series4.2s

Counts
4 → 12
Calls
4 calls:
755.0ms
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
3.1s
(/.f64 (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
129.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
200.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify142.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0512516401

prune457.0ms

Filtered
175 candidates to 265 candidates (-51.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2641265
Fresh178
Picked101
Done011
Total2669275

Merged error: 33.8b

Counts
275 → 9

regimes109.0ms

Accuracy

25.1% (2.8b remaining)

Error of 36.5b against oracle of 33.6b and baseline of 37.4b

bsearch42.0ms

Steps
ItersRangePoint
10
3.096694167984224e+172
8.811531502303727e+187
3.3288565842443027e+172

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046111
146111

end0.0ms

sample927.0ms

Algorithm
intervals
Results
600.0ms8000×body128valid
161.0ms8000×pre128true

Profiling

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