Details

Time bar (total: 19.4s)

analyze46.0ms (0.2%)

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
Compiler

Compiled 63 to 34 computations (46% saved)

sample36.0ms (0.2%)

Algorithm
intervals
Results
20.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify43.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0539479

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 55.5b

Counts
2 → 1
Compiler

Compiled 106 to 54 computations (49.1% saved)

localize17.0ms (0.1%)

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))))
36.6b
(/.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))
47.8b
(/.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))))

rewrite157.0ms (0.8%)

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:

42.0ms
(/.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))
27.0ms
(/.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))))
19.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
15.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series3.7s (18.9%)

Counts
4 → 12
Calls

4 calls:

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))
397.0ms
(/.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))))
220.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
105.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify148.0ms (0.8%)

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0525518181

prune906.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2337240
Fresh000
Picked011
Done000
Total2338241

Merged error: 34.1b

Counts
241 → 8
Compiler

Compiled 25575 to 10555 computations (58.7% saved)

localize18.0ms (0.1%)

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)))
35.5b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
37.0b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite281.0ms (1.4%)

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:

123.0ms
(*.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)))
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))
16.0ms
(/.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 (19.7%)

Counts
4 → 12
Calls

4 calls:

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)))
369.0ms
(/.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))
198.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
124.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify225.0ms (1.2%)

Algorithm
egg-herbie
Counts
407 → 407
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0513930002

prune1.7s (8.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4025407
Fresh426
Picked101
Done011
Total4078415

Merged error: 34.0b

Counts
415 → 8
Compiler

Compiled 38211 to 16160 computations (57.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
0.0b
(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
0.1b
(*.f64 (/.f64 (*.f64 i (/.f64 (+.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)))
37.0b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite192.0ms (1%)

Algorithm
rewrite-expression-head
Rules
215×times-frac_binary64
181×*-un-lft-identity_binary64
173×add-sqr-sqrt_binary64
132×associate-*r*_binary64
99×add-cube-cbrt_binary64
67×add-exp-log_binary64 add-cbrt-cube_binary64
30×difference-of-squares_binary64
27×cbrt-undiv_binary64 div-exp_binary64
24×associate-/r/_binary64
22×distribute-lft-out_binary64
20×cbrt-unprod_binary64 prod-exp_binary64
15×difference-of-sqr-1_binary64 distribute-lft-out--_binary64
13×flip3-+_binary64 associate-*l*_binary64 flip-+_binary64
12×div-inv_binary64
pow1_binary64 associate-/l*_binary64
associate-/r*_binary64
unswap-sqr_binary64
associate-/l/_binary64 add-log-exp_binary64
pow-prod-down_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
flip3--_binary64 flip--_binary64 frac-times_binary64 associate-*l/_binary64
Counts
4 → 270
Calls

4 calls:

80.0ms
(*.f64 (/.f64 (*.f64 i (/.f64 (+.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)))
24.0ms
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
13.0ms
(/.f64 (+.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)))

series3.5s (18%)

Counts
4 → 12
Calls

4 calls:

3.1s
(*.f64 (/.f64 (*.f64 i (/.f64 (+.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)))
212.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
122.0ms
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
80.0ms
(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify171.0ms (0.9%)

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0503717008

prune935.0ms (4.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2802282
Fresh246
Picked011
Done011
Total2828290

Merged error: 2.0b

Counts
290 → 8
Compiler

Compiled 22409 to 9438 computations (57.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (/.f64 (*.f64 i (/.f64 (+.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 1/4) (+.f64 (*.f64 i 1/2) (*.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
0.0b
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)
0.0b
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
0.0b
(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite122.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
85×*-un-lft-identity_binary64
59×add-sqr-sqrt_binary64
57×times-frac_binary64
48×associate-*r*_binary64
43×add-exp-log_binary64 add-cbrt-cube_binary64
37×add-cube-cbrt_binary64
23×distribute-lft-out_binary64
14×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
13×add-log-exp_binary64 associate-*l*_binary64
pow1_binary64 associate-/r/_binary64
difference-of-squares_binary64 sum-log_binary64
flip3-+_binary64 associate-/l*_binary64 flip-+_binary64
unswap-sqr_binary64 div-inv_binary64
associate-/r*_binary64 difference-of-sqr-1_binary64 distribute-lft-out--_binary64
pow-prod-down_binary64 associate-/l/_binary64 associate-*r/_binary64 *-commutative_binary64
flip3--_binary64 associate-+l+_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 flip--_binary64 frac-times_binary64 associate-*l/_binary64
Counts
4 → 161
Calls

4 calls:

47.0ms
(*.f64 (/.f64 (*.f64 i (/.f64 (+.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 1/4) (+.f64 (*.f64 i 1/2) (*.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
19.0ms
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
13.0ms
(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
9.0ms
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)

series711.0ms (3.7%)

Counts
4 → 12
Calls

4 calls:

461.0ms
(*.f64 (/.f64 (*.f64 i (/.f64 (+.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 1/4) (+.f64 (*.f64 i 1/2) (*.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
124.0ms
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
93.0ms
(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.0ms
(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)

simplify91.0ms (0.5%)

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
053407009

prune751.0ms (3.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1694173
Fresh055
Picked101
Done022
Total17011181

Merged error: 2.0b

Counts
181 → 11
Compiler

Compiled 21499 to 10514 computations (51.1% saved)

regimes205.0ms (1.1%)

Compiler

Compiled 2584 to 1448 computations (44% saved)

bsearch200.0ms (1%)

Steps
ItersRangePoint
10
1.8913417392039433e+212
2.568845296500658e+223
1.921741030358534e+212
10
4.7552713829279884e+145
3.226617956057658e+157
3.173964194173191e+157
9
1.5516714456166342e+88
5.263923327004482e+94
2.0833052166247658e+88
6
-8.544872215306305e-173
-5.605877297528356e-174
-2.139573966778813e-173
9
-9.332151444135382e-115
-7.406330214616513e-124
-9.765822633999939e-119
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
081423
181423

end0.0ms (0%)

sample1.4s (7.4%)

Algorithm
intervals
Results
627.0ms8000×body128valid
185.0ms8000×pre128true
Compiler

Compiled 965 to 511 computations (47% saved)

Profiling

Loading profile data...