Details

Time bar (total: 6.7s)

analyze47.0ms (0.7%)

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)

sample35.0ms (0.5%)

Algorithm
intervals
Results
20.0ms256×body80valid
6.0ms256×pre80true
Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify34.0ms (0.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0498179
1498179

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 55.7b

Counts
2 → 1
Compiler

Compiled 106 to 54 computations (49.1% saved)

localize20.0ms (0.3%)

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))))
33.6b
(/.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))
48.0b
(/.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))))

rewrite113.0ms (1.7%)

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))
28.0ms
(/.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))))
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))))

series492.0ms (7.3%)

Counts
4 → 12
Calls

4 calls:

387.0ms
(/.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))
63.0ms
(/.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))))
29.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
13.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify189.0ms (2.8%)

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0499118186
1499118186

prune480.0ms (7.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2337240
Fresh000
Picked101
Done000
Total2347241

Merged error: 31.8b

Counts
241 → 7
Compiler

Compiled 17727 to 6675 computations (62.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(/.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))
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)))
33.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
33.9b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite179.0ms (2.7%)

Algorithm
rewrite-expression-head
Rules
288×times-frac_binary64
200×*-un-lft-identity_binary64
198×add-sqr-sqrt_binary64
117×add-cube-cbrt_binary64
111×associate-*r*_binary64
74×add-exp-log_binary64 add-cbrt-cube_binary64
42×associate-/r/_binary64 associate-*l*_binary64
35×cbrt-undiv_binary64 div-exp_binary64
30×difference-of-squares_binary64
22×flip3-+_binary64 flip-+_binary64
21×div-inv_binary64
19×distribute-lft-out_binary64
17×cbrt-unprod_binary64 prod-exp_binary64
15×difference-of-sqr-1_binary64 distribute-lft-out--_binary64
13×associate-/l*_binary64
10×associate-/r*_binary64
pow1_binary64 unswap-sqr_binary64
associate-/l/_binary64
add-log-exp_binary64
associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64
pow-prod-down_binary64 flip3--_binary64 flip--_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 319
Calls

4 calls:

111.0ms
(*.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)))
22.0ms
(/.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))
14.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
12.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series443.0ms (6.6%)

Counts
4 → 12
Calls

4 calls:

365.0ms
(*.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)))
33.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
28.0ms
(/.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))
16.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify219.0ms (3.2%)

Algorithm
egg-herbie
Counts
331 → 331
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0498022529
1498022529

prune720.0ms (10.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3265331
Fresh156
Picked101
Done000
Total32810338

Merged error: 31.8b

Counts
338 → 10
Compiler

Compiled 25454 to 10504 computations (58.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.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 alpha beta) (*.f64 i 2)) 1))
0.1b
(*.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.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)))
33.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
33.9b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite128.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
85×add-exp-log_binary64 add-cbrt-cube_binary64
80×times-frac_binary64
65×*-un-lft-identity_binary64
61×add-sqr-sqrt_binary64
42×associate-*r*_binary64
41×add-cube-cbrt_binary64
40×cbrt-undiv_binary64 div-exp_binary64
21×cbrt-unprod_binary64 prod-exp_binary64
18×associate-/r/_binary64
15×associate-*l*_binary64
13×associate-/r*_binary64
10×flip3-+_binary64 flip-+_binary64
distribute-lft-out_binary64 div-inv_binary64
associate-/l/_binary64
pow1_binary64
associate-/l*_binary64
add-log-exp_binary64 associate-*r/_binary64 unswap-sqr_binary64 difference-of-squares_binary64
clear-num_binary64 frac-2neg_binary64
difference-of-sqr-1_binary64 distribute-lft-out--_binary64 frac-times_binary64 associate-*l/_binary64
pow-prod-down_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64
Counts
4 → 193
Calls

4 calls:

49.0ms
(*.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.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)))
44.0ms
(/.f64 (*.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.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 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)))

series319.0ms (4.7%)

Counts
4 → 12
Calls

4 calls:

152.0ms
(*.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.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)))
118.0ms
(/.f64 (*.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (/.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 alpha beta) (*.f64 i 2)) 1))
33.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
17.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify149.0ms (2.2%)

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0500412015

prune348.0ms (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2041205
Fresh279
Picked011
Done000
Total2069215

Merged error: 31.8b

Counts
215 → 9
Compiler

Compiled 14136 to 5772 computations (59.2% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

33.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
33.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
33.9b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
33.9b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite55.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 times-frac_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
12×associate-/r*_binary64
flip3-+_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 flip-+_binary64
cbrt-undiv_binary64 div-exp_binary64
add-log-exp_binary64 pow1_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64
cbrt-unprod_binary64 prod-exp_binary64
Counts
4 → 112
Calls

4 calls:

14.0ms
(/.f64 (*.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)))
12.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
12.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series96.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

33.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
30.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
17.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
16.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify111.0ms (1.6%)

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049633910
149633910

prune421.0ms (6.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1240124
Fresh077
Picked011
Done011
Total1249133

Merged error: 31.8b

Counts
133 → 9
Compiler

Compiled 15950 to 6846 computations (57.1% saved)

regimes222.0ms (3.3%)

Compiler

Compiled 1638 to 900 computations (45.1% saved)

bsearch26.0ms (0.4%)

Steps
ItersRangePoint
8
2.3889619945398835e+200
4.1584489121950635e+204
2.7247229081146494e+201
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04489
14489

end0.0ms (0%)

sample1.8s (27%)

Algorithm
intervals
Results
658.0ms8000×body80valid
172.0ms8000×pre80true
Compiler

Compiled 667 to 364 computations (45.4% saved)

Profiling

Loading profile data...