Details

Time bar (total: 14.4s)

analyze169.0ms (1.2%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05646316
033
133
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)

sample39.0ms (0.3%)

Algorithm
intervals
Results
23.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify42.0ms (0.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0539579

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 55.0b

Counts
2 → 1
Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (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))))
35.5b
(/.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))
47.2b
(/.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))))

rewrite155.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
86×times-frac_binary64_1789
66×associate-/r/_binary64_1729 flip-+_binary64_1757 flip3-+_binary64_1786
61×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
46×add-sqr-sqrt_binary64_1805
44×*-un-lft-identity_binary64_1783 frac-times_binary64_1793
34×associate-*r/_binary64_1725
30×add-cube-cbrt_binary64_1818
28×difference-of-squares_binary64_1752
22×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l/_binary64_1726
19×cbrt-undiv_binary64_1817 div-exp_binary64_1834
16×pow1_binary64_1844
14×associate-/l*_binary64_1728 difference-of-sqr-1_binary64_1753
associate-/l/_binary64_1730 div-inv_binary64_1780
associate-/r*_binary64_1727
associate-*r*_binary64_1723
associate-*l*_binary64_1724 pow-prod-down_binary64_1854 add-log-exp_binary64_1822
swap-sqr_binary64_1750
distribute-lft-in_binary64_1732 *-commutative_binary64_1714 frac-2neg_binary64_1794 distribute-rgt-in_binary64_1733 clear-num_binary64_1782
flip3--_binary64_1787 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow-sqr_binary64_1756 unswap-sqr_binary64_1751 flip--_binary64_1758 pow2_binary64_1864
Counts
4 → 228
Calls

4 calls:

46.0ms
(/.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))
26.0ms
(/.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))))

series1.9s (13.2%)

Counts
4 → 12
Calls

4 calls:

1.5s
(/.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))
209.0ms
(/.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))))
91.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
55.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify153.0ms (1.1%)

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0526118181

prune691.0ms (4.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2346240
Fresh000
Picked101
Done000
Total2356241

Merged error: 32.8b

Counts
241 → 6
Compiler

Compiled 17659 to 6632 computations (62.4% saved)

localize22.0ms (0.2%)

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)))
34.1b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
35.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite263.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
414×times-frac_binary64_1789
314×add-sqr-sqrt_binary64_1805
280×*-un-lft-identity_binary64_1783
169×add-cube-cbrt_binary64_1818
111×associate-*r*_binary64_1723
70×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
62×difference-of-squares_binary64_1752
48×associate-/r/_binary64_1729
42×associate-*l*_binary64_1724
33×cbrt-undiv_binary64_1817 div-exp_binary64_1834
31×difference-of-sqr-1_binary64_1753 distribute-lft-out--_binary64_1735
24×flip-+_binary64_1757 div-inv_binary64_1780 flip3-+_binary64_1786
19×associate-/l*_binary64_1728
16×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
13×associate-/r*_binary64_1727
distribute-lft-out_binary64_1734
unswap-sqr_binary64_1751 pow1_binary64_1844
associate-/l/_binary64_1730
add-log-exp_binary64_1822
associate-*r/_binary64_1725 frac-2neg_binary64_1794 clear-num_binary64_1782
flip3--_binary64_1787 flip--_binary64_1758
associate-*l/_binary64_1726 *-commutative_binary64_1714 frac-times_binary64_1793 pow-prod-down_binary64_1854
Counts
4 → 395
Calls

4 calls:

124.0ms
(*.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)))
24.0ms
(/.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))
13.0ms
(/.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)))

series1.9s (13.3%)

Counts
4 → 12
Calls

4 calls:

1.5s
(*.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)))
196.0ms
(/.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))
107.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
68.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify232.0ms (1.6%)

Algorithm
egg-herbie
Counts
407 → 407
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0517030002

prune1.6s (11%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4025407
Fresh325
Picked101
Done000
Total4067413

Merged error: 32.7b

Counts
413 → 7
Compiler

Compiled 32150 to 13011 computations (59.5% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

34.1b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
34.1b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
35.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
35.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite79.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783 times-frac_binary64_1789
18×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
12×associate-/r*_binary64_1727
associate-/l/_binary64_1730 associate-/r/_binary64_1729 associate-/l*_binary64_1728 flip-+_binary64_1757 flip3-+_binary64_1786
cbrt-undiv_binary64_1817 div-exp_binary64_1834
associate-*r/_binary64_1725 div-inv_binary64_1780 frac-2neg_binary64_1794 clear-num_binary64_1782 add-log-exp_binary64_1822 pow1_binary64_1844
cbrt-unprod_binary64_1816 prod-exp_binary64_1832
Counts
4 → 112
Calls

4 calls:

14.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
13.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
13.0ms
(/.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)))

series333.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

112.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
101.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
62.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
58.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify91.0ms (0.6%)

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050313910

prune567.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1240124
Fresh066
Picked011
Done000
Total1247131

Merged error: 32.7b

Counts
131 → 7
Compiler

Compiled 15763 to 6528 computations (58.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))
0.2b
(*.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 1 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
34.1b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
35.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite191.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
220×add-exp-log_binary64_1821
136×add-cbrt-cube_binary64_1819
94×times-frac_binary64_1789
91×div-exp_binary64_1834
87×prod-exp_binary64_1832
77×*-un-lft-identity_binary64_1783
74×add-sqr-sqrt_binary64_1805
69×associate-*r*_binary64_1723
54×cbrt-undiv_binary64_1817
50×add-cube-cbrt_binary64_1818
49×cbrt-unprod_binary64_1816
18×associate-/r/_binary64_1729
16×associate-*l*_binary64_1724
11×pow1_binary64_1844
10×flip-+_binary64_1757 flip3-+_binary64_1786
distribute-lft-out_binary64_1734 1-exp_binary64_1827 div-inv_binary64_1780 rec-exp_binary64_1833
associate-*r/_binary64_1725 difference-of-squares_binary64_1752 associate-/r*_binary64_1727 associate-*l/_binary64_1726 frac-times_binary64_1793
associate-/l/_binary64_1730 associate-/l*_binary64_1728 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751 add-log-exp_binary64_1822
difference-of-sqr-1_binary64_1753 distribute-lft-out--_binary64_1735
*-commutative_binary64_1714 frac-2neg_binary64_1794 clear-num_binary64_1782
flip3--_binary64_1787 un-div-inv_binary64_1781 flip--_binary64_1758
Counts
4 → 245
Calls

4 calls:

60.0ms
(*.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 1 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
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)))
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)))

series1.2s (8.1%)

Counts
4 → 12
Calls

4 calls:

552.0ms
(*.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)))
441.0ms
(*.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 1 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
104.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
69.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify169.0ms (1.2%)

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0506615906

prune611.0ms (4.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2570257
Fresh055
Picked011
Done011
Total2577264

Merged error: 32.7b

Counts
264 → 7
Compiler

Compiled 16836 to 7111 computations (57.8% saved)

regimes952.0ms (6.6%)

Compiler

Compiled 17968 to 9273 computations (48.4% saved)

bsearch23.0ms (0.2%)

Steps
ItersRangePoint
4
1.1075556308085377e+191
1.645968222872371e+191
1.335095226471943e+191
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04589
14589

end0.0ms (0%)

sample3.0s (20.8%)

Algorithm
intervals
Results
633.0ms8000×body128valid
191.0ms8000×pre128true
Compiler

Compiled 4547 to 2350 computations (48.3% saved)

Profiling

Loading profile data...