Details

Time bar (total: 31.7s)

analyze44.0ms (0.1%)

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 (0.1%)

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

Compiled 116 to 64 computations (44.8% saved)

simplify202.0ms (0.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0539579

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 53.5b

Counts
2 → 1
Compiler

Compiled 106 to 54 computations (49.1% saved)

localize15.0ms (0%)

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))))
34.6b
(/.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))
45.9b
(/.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 (0.5%)

Algorithm
rewrite-expression-head
Rules
86×times-frac_binary64_1805
66×associate-/r/_binary64_1745 flip3-+_binary64_1802 flip-+_binary64_1773
61×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
46×add-sqr-sqrt_binary64_1821
44×*-un-lft-identity_binary64_1799 frac-times_binary64_1809
34×associate-*r/_binary64_1741
30×add-cube-cbrt_binary64_1834
28×difference-of-squares_binary64_1768
22×prod-exp_binary64_1848 cbrt-unprod_binary64_1832 associate-*l/_binary64_1742
19×div-exp_binary64_1850 cbrt-undiv_binary64_1833
16×pow1_binary64_1860
14×associate-/l*_binary64_1744 difference-of-sqr-1_binary64_1769
associate-/l/_binary64_1746 div-inv_binary64_1796
associate-/r*_binary64_1743
associate-*r*_binary64_1739
add-log-exp_binary64_1838 associate-*l*_binary64_1740 pow-prod-down_binary64_1870
swap-sqr_binary64_1766
distribute-rgt-in_binary64_1749 clear-num_binary64_1798 distribute-lft-in_binary64_1748 frac-2neg_binary64_1810 *-commutative_binary64_1730
pow2_binary64_1880 pow-sqr_binary64_1772 unswap-sqr_binary64_1767 flip--_binary64_1774 flip3--_binary64_1803 pow-prod-up_binary64_1869 pow-plus_binary64_1862
Counts
4 → 228
Calls

4 calls:

47.0ms
(/.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))))
15.0ms
(*.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))))

series3.5s (11%)

Counts
4 → 12
Calls

4 calls:

2.8s
(/.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))
388.0ms
(/.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))))
198.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
94.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify154.0ms (0.5%)

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0525518181

prune958.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2328240
Fresh000
Picked101
Done000
Total2338241

Merged error: 31.6b

Counts
241 → 8
Compiler

Compiled 27674 to 11610 computations (58% saved)

localize17.0ms (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)))
32.3b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.7b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite274.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
414×times-frac_binary64_1805
314×add-sqr-sqrt_binary64_1821
280×*-un-lft-identity_binary64_1799
169×add-cube-cbrt_binary64_1834
111×associate-*r*_binary64_1739
70×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
62×difference-of-squares_binary64_1768
48×associate-/r/_binary64_1745
42×associate-*l*_binary64_1740
33×div-exp_binary64_1850 cbrt-undiv_binary64_1833
31×difference-of-sqr-1_binary64_1769 distribute-lft-out--_binary64_1751
24×div-inv_binary64_1796 flip3-+_binary64_1802 flip-+_binary64_1773
19×associate-/l*_binary64_1744
16×prod-exp_binary64_1848 cbrt-unprod_binary64_1832
13×associate-/r*_binary64_1743
distribute-lft-out_binary64_1750
pow1_binary64_1860 unswap-sqr_binary64_1767
associate-/l/_binary64_1746
add-log-exp_binary64_1838
clear-num_binary64_1798 frac-2neg_binary64_1810 associate-*r/_binary64_1741
flip--_binary64_1774 flip3--_binary64_1803
*-commutative_binary64_1730 pow-prod-down_binary64_1870 frac-times_binary64_1809 associate-*l/_binary64_1742
Counts
4 → 395
Calls

4 calls:

126.0ms
(*.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))
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)))

series3.9s (12.2%)

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)))
388.0ms
(/.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))
211.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
127.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify235.0ms (0.7%)

Algorithm
egg-herbie
Counts
407 → 407
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0513930002

prune1.8s (5.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4034407
Fresh347
Picked011
Done000
Total4069415

Merged error: 31.6b

Counts
415 → 9
Compiler

Compiled 44717 to 19403 computations (56.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
13.0b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
19.5b
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
32.3b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite1.4s (4.4%)

Algorithm
rewrite-expression-head
Rules
3195×times-frac_binary64_1805
1894×add-sqr-sqrt_binary64_1821
1688×*-un-lft-identity_binary64_1799
1220×add-cube-cbrt_binary64_1834
1056×associate-*r*_binary64_1739
1042×sqrt-prod_binary64_1815
300×difference-of-squares_binary64_1768
150×difference-of-sqr-1_binary64_1769 distribute-lft-out--_binary64_1751
130×associate-/r/_binary64_1745
116×sqrt-div_binary64_1816
96×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
66×flip3-+_binary64_1802 flip-+_binary64_1773
65×div-inv_binary64_1796
50×div-exp_binary64_1850 cbrt-undiv_binary64_1833
42×associate-*l*_binary64_1740
28×associate-/l*_binary64_1744
21×prod-exp_binary64_1848 cbrt-unprod_binary64_1832
16×unswap-sqr_binary64_1767
15×associate-/r*_binary64_1743
distribute-lft-out_binary64_1750
pow1_binary64_1860
associate-/l/_binary64_1746
add-log-exp_binary64_1838
clear-num_binary64_1798 frac-2neg_binary64_1810 associate-*r/_binary64_1741
flip--_binary64_1774 flip3--_binary64_1803 *-commutative_binary64_1730 pow-prod-down_binary64_1870 frac-times_binary64_1809 associate-*l/_binary64_1742
Counts
4 → 1417
Calls

4 calls:

790.0ms
(*.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 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
25.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
17.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
14.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

series4.0s (12.5%)

Counts
4 → 12
Calls

4 calls:

3.2s
(*.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 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
433.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
245.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
127.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify986.0ms (3.1%)

Algorithm
egg-herbie
Counts
1429 → 1429
Iterations

Useful iterations: 0 (108.0ms)

IterNodesCost
04973129636
14973129636

prune11.1s (35.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New142901429
Fresh077
Picked011
Done011
Total142991438

Merged error: 31.6b

Counts
1438 → 9
Compiler

Compiled 143497 to 62054 computations (56.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

32.3b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.7b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.7b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.7b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite88.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt_binary64_1821 add-cube-cbrt_binary64_1834 *-un-lft-identity_binary64_1799 times-frac_binary64_1805
15×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
12×associate-/r*_binary64_1743
10×associate-/l*_binary64_1744
associate-/r/_binary64_1745 associate-/l/_binary64_1746 flip3-+_binary64_1802 flip-+_binary64_1773
div-exp_binary64_1850 cbrt-undiv_binary64_1833
pow1_binary64_1860 clear-num_binary64_1798 add-log-exp_binary64_1838 frac-2neg_binary64_1810 div-inv_binary64_1796
associate-*r/_binary64_1741
prod-exp_binary64_1848 cbrt-unprod_binary64_1832
Counts
4 → 118
Calls

4 calls:

14.0ms
(/.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)))
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)))

series716.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

202.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.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)))
194.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
120.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify94.0ms (0.3%)

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049784535
149784535

prune588.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1300130
Fresh066
Picked011
Done022
Total1309139

Merged error: 31.6b

Counts
139 → 9
Compiler

Compiled 17179 to 6931 computations (59.7% saved)

regimes111.0ms (0.4%)

Compiler

Compiled 1734 to 882 computations (49.1% saved)

bsearch26.0ms (0.1%)

Steps
ItersRangePoint
6
6.377019590634338e+222
3.0244135843059206e+223
6.675875267470258e+222
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04389
14389

end0.0ms (0%)

sample1.3s (4.2%)

Algorithm
intervals
Results
632.0ms8000×body128valid
184.0ms8000×pre128true
Compiler

Compiled 699 to 358 computations (48.8% saved)

Profiling

Loading profile data...