Details

Time bar (total: 18.5min)

analyze124.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample37.0ms (0%)

Algorithm
1×intervals
Results
11.0ms200×body128valid
6.0ms256×pre128true
5.0ms22×body1024valid
3.0ms16×body512valid
2.0ms14×body256valid
1.0ms4×body2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify167.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
0537143

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
27.4b
Counts
2 → 1
Compiler

Compiled 29 to 20 computations (31% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
2.3b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
0.0b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
2.3b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite107.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
56×*-un-lft-identity_binary64_1783
54×times-frac_binary64_1789
34×add-sqr-sqrt_binary64_1805
30×add-cube-cbrt_binary64_1818
20×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
14×associate-/r/_binary64_1729 flip-+_binary64_1757 flip3-+_binary64_1786
12×distribute-lft-out_binary64_1734
10×associate-/l*_binary64_1728
9×associate-/l/_binary64_1730
8×frac-times_binary64_1793
7×div-inv_binary64_1780 associate-/r*_binary64_1727 cbrt-undiv_binary64_1817 div-exp_binary64_1834
6×flip3--_binary64_1787 cancel-sign-sub-inv_binary64_1749 flip--_binary64_1758 add-log-exp_binary64_1822 pow1_binary64_1844
5×associate-*r*_binary64_1723
4×associate-*r/_binary64_1725 distribute-lft-in_binary64_1732 associate-*l*_binary64_1724 associate-*l/_binary64_1726 distribute-rgt-in_binary64_1733
3×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
2×frac-2neg_binary64_1794 clear-num_binary64_1782 sub-neg_binary64_1776
1×difference-of-squares_binary64_1752 +-commutative_binary64_1713 distribute-lft-out--_binary64_1735 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
Counts
4 → 148
Calls

8 calls:

39.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
17.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
10.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series2.9s (0.3%)

Counts
4 → 73
Calls

4 calls:

1.8s
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
792.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
185.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
121.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
Compiler

Compiled 7960 to 6189 computations (22.2% saved)

simplify112.0ms (0%)

Algorithm
1×egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0502410109

prune1.8s (0.2%)

Pruning

113 alts after pruning (112 fresh and 1 done)

PrunedKeptTotal
New109112221
Fresh000
Picked000
Done011
Total109113222
Error
0.1b
Counts
222 → 113
Compiler

Compiled 13252 to 7701 computations (41.9% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

4.0b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
3.0b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
3.0b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
4.0b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite152.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
321×times-frac_binary64_1789
290×*-un-lft-identity_binary64_1783
211×add-sqr-sqrt_binary64_1805
140×add-cube-cbrt_binary64_1818
90×associate-*r*_binary64_1723
44×distribute-lft-out_binary64_1734
31×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
26×associate-/l*_binary64_1728
24×associate-/r/_binary64_1729
20×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
15×flip-+_binary64_1757 flip3-+_binary64_1786
12×div-inv_binary64_1780
7×associate-/r*_binary64_1727 cbrt-undiv_binary64_1817 div-exp_binary64_1834
6×add-log-exp_binary64_1822 pow1_binary64_1844
4×associate-*l*_binary64_1724
3×div-sub_binary64_1788 associate-/l/_binary64_1730 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 unswap-sqr_binary64_1751
2×associate-*l/_binary64_1726 frac-2neg_binary64_1794 frac-times_binary64_1793 clear-num_binary64_1782
1×flip3--_binary64_1787 associate-*r/_binary64_1725 +-commutative_binary64_1713 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854 flip--_binary64_1758
Counts
4 → 295
Calls

8 calls:

41.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
30.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
25.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
11.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series3.5s (0.3%)

Counts
4 → 81
Calls

4 calls:

1.9s
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
785.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
678.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
166.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 9981 to 7686 computations (23% saved)

simplify171.0ms (0%)

Algorithm
1×egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0508418850

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

1.4b
(-.f64 (*.f64 alpha alpha) (*.f64 beta beta))
1.4b
(-.f64 (*.f64 alpha alpha) (*.f64 beta beta))
0.1b
(*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha)))
0.0b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.4b
(-.f64 (*.f64 alpha alpha) (*.f64 beta beta))
2.2b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))
5.2b
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
36.5b
(/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta))))

rewrite100.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
13×flip3--_binary64_1787 flip--_binary64_1758
12×frac-times_binary64_1793
8×associate-/l/_binary64_1730 associate-/r/_binary64_1729 add-sqr-sqrt_binary64_1805 *-un-lft-identity_binary64_1783 add-log-exp_binary64_1822
7×flip-+_binary64_1757 flip3-+_binary64_1786
6×associate-*r/_binary64_1725 add-cube-cbrt_binary64_1818 associate-*l/_binary64_1726 pow1_binary64_1844
5×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
4×cbrt-undiv_binary64_1817 div-exp_binary64_1834 associate-*r*_binary64_1723
3×cancel-sign-sub-inv_binary64_1749 associate-*l*_binary64_1724 sub-neg_binary64_1776
2×difference-of-squares_binary64_1752 distribute-lft-in_binary64_1732 distribute-rgt-in_binary64_1733
1×+-commutative_binary64_1713 associate-/l*_binary64_1728 distribute-lft-out_binary64_1734 div-inv_binary64_1780 associate-/r*_binary64_1727 diff-log_binary64_1875 times-frac_binary64_1789 *-commutative_binary64_1714 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
Counts
4 → 93
Calls

8 calls:

47.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.0ms
(/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta))))
12.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))
4.0ms
(-.f64 (*.f64 alpha alpha) (*.f64 beta beta))
0.0ms
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

series2.4s (0.2%)

Counts
4 → 81
Calls

4 calls:

1.9s
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
238.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)))
205.0ms
(/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (*.f64 beta beta) (*.f64 alpha alpha))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 (*.f64 alpha alpha) (*.f64 beta beta))))
109.0ms
(-.f64 (*.f64 alpha alpha) (*.f64 beta beta))
Compiler

Compiled 7347 to 5399 computations (26.5% saved)

simplify84.0ms (0%)

Algorithm
1×egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
053497639

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.3b
(/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
5.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
9.5b
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
18.0b
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))

rewrite223.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
369×times-frac_binary64_1789
249×*-un-lft-identity_binary64_1783
201×add-sqr-sqrt_binary64_1805
179×add-cube-cbrt_binary64_1818
139×sqrt-prod_binary64_1799
111×associate-*r*_binary64_1723
78×add-exp-log_binary64_1821
50×add-cbrt-cube_binary64_1819
38×associate-/r/_binary64_1729
36×div-exp_binary64_1834
34×distribute-lft-out_binary64_1734
23×flip-+_binary64_1757 flip3-+_binary64_1786
21×prod-exp_binary64_1832
20×cbrt-undiv_binary64_1817
19×div-inv_binary64_1780
16×associate-/l*_binary64_1728
14×associate-/r*_binary64_1727
13×cbrt-unprod_binary64_1816 associate-*l*_binary64_1724
9×associate-/l/_binary64_1730
8×sqrt-div_binary64_1800
7×unswap-sqr_binary64_1751
6×add-log-exp_binary64_1822 pow1_binary64_1844
5×frac-times_binary64_1793
4×1-exp_binary64_1827 rec-exp_binary64_1833
3×flip3--_binary64_1787 associate-*r/_binary64_1725 associate-*l/_binary64_1726 flip--_binary64_1758
2×frac-2neg_binary64_1794 clear-num_binary64_1782
1×+-commutative_binary64_1713 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854
Counts
4 → 363
Calls

8 calls:

70.0ms
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
42.0ms
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
18.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
18.0ms
(/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series3.2s (0.3%)

Counts
4 → 64
Calls

4 calls:

1.9s
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
825.0ms
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
271.0ms
(/.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
205.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 8661 to 6689 computations (22.8% saved)

simplify265.0ms (0%)

Algorithm
1×egg-herbie
Counts
427 → 427
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
0497624310
1497624310

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
13.3b
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite105.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
57×times-frac_binary64_1789
46×*-un-lft-identity_binary64_1783
42×cbrt-prod_binary64_1814
28×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818
24×associate-/l/_binary64_1730
19×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
17×flip-+_binary64_1757 flip3-+_binary64_1786
16×associate-/r/_binary64_1729
12×frac-times_binary64_1793
9×flip3--_binary64_1787 distribute-lft-out_binary64_1734 associate-/r*_binary64_1727 flip--_binary64_1758
8×div-inv_binary64_1780
6×associate-*r/_binary64_1725 associate-*l/_binary64_1726 cbrt-undiv_binary64_1817 div-exp_binary64_1834
4×add-log-exp_binary64_1822 pow1_binary64_1844
3×associate-/l*_binary64_1728 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 frac-2neg_binary64_1794 clear-num_binary64_1782
1×cbrt-div_binary64_1815 pow1/3_binary64_1865
Counts
4 → 144
Calls

8 calls:

25.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series1.6s (0.1%)

Counts
4 → 66
Calls

4 calls:

986.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
222.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
220.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
214.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 10711 to 6739 computations (37.1% saved)

simplify105.0ms (0%)

Algorithm
1×egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049787520
149787520

prune36.6s (3.3%)

Pruning

553 alts after pruning (548 fresh and 5 done)

PrunedKeptTotal
New7294581187
Fresh1790107
Picked000
Done156
Total7475531300
Error
0.1b
Counts
1300 → 553
Compiler

Compiled 85863 to 47942 computations (44.2% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

3.0b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.4b
(/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.1b
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.4b
(/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.0b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
4.0b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite1.2s (0.1%)

Algorithm
1×rewrite-expression-head
Rules
8014×times-frac_binary64_1789
4762×*-un-lft-identity_binary64_1783
3632×add-sqr-sqrt_binary64_1805
2892×add-cube-cbrt_binary64_1818
1162×associate-*r*_binary64_1723
590×distribute-lft-out_binary64_1734
339×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
322×div-inv_binary64_1780
256×associate-/r/_binary64_1729
152×add-exp-log_binary64_1821
117×flip-+_binary64_1757 flip3-+_binary64_1786
111×div-exp_binary64_1834
110×associate-/r*_binary64_1727
59×add-cbrt-cube_binary64_1819
33×cbrt-undiv_binary64_1817
30×1-exp_binary64_1827
22×prod-exp_binary64_1832
17×associate-/l*_binary64_1728
16×unswap-sqr_binary64_1751
12×rec-exp_binary64_1833
7×cbrt-unprod_binary64_1816
6×add-log-exp_binary64_1822 pow1_binary64_1844
4×associate-*l*_binary64_1724
3×associate-/l/_binary64_1730
2×associate-*l/_binary64_1726 frac-2neg_binary64_1794 frac-times_binary64_1793 clear-num_binary64_1782
1×associate-*r/_binary64_1725 +-commutative_binary64_1713 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854
Counts
4 → 1000
Calls

8 calls:

327.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
104.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
61.0ms
(/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
20.0ms
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series3.9s (0.3%)

Counts
4 → 89
Calls

4 calls:

1.9s
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
817.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
692.0ms
(/.f64 (/.f64 1 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
479.0ms
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 10927 to 8351 computations (23.6% saved)

simplify418.0ms (0%)

Algorithm
1×egg-herbie
Counts
1089 → 1089
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0532749946

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3)))
0.0b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.0b
(*.f64 alpha (+.f64 alpha beta))
0.0b
(+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta)))
1.8b
(-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))
3.5b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))
5.7b
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
41.7b
(/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta))))

rewrite195.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
60×frac-times_binary64_1793
37×flip-+_binary64_1757 flip3-+_binary64_1786
36×add-sqr-sqrt_binary64_1805
30×add-cbrt-cube_binary64_1819 associate-*r/_binary64_1725 add-exp-log_binary64_1821
26×associate-/r/_binary64_1729
25×flip3--_binary64_1787 flip--_binary64_1758
24×cancel-sign-sub-inv_binary64_1749 *-un-lft-identity_binary64_1783
18×associate-*l/_binary64_1726
16×difference-of-squares_binary64_1752 distribute-lft-in_binary64_1732 distribute-rgt-in_binary64_1733
15×unpow-prod-down_binary64_1862 cube-prod_binary64_1811
12×add-cube-cbrt_binary64_1818 cbrt-unprod_binary64_1816 prod-exp_binary64_1832
9×sqr-pow_binary64_1755 pow1_binary64_1844
8×associate-/l/_binary64_1730 add-log-exp_binary64_1822
6×cbrt-undiv_binary64_1817 div-exp_binary64_1834
5×distribute-lft-out--_binary64_1735 sub-neg_binary64_1776
3×associate-*l*_binary64_1724 pow-prod-down_binary64_1854
1×+-commutative_binary64_1713 associate-/l*_binary64_1728 cube-mult_binary64_1813 distribute-lft-out_binary64_1734 unpow3_binary64_1849 div-inv_binary64_1780 associate-/r*_binary64_1727 difference-cubes_binary64_1785 diff-log_binary64_1875 times-frac_binary64_1789 *-commutative_binary64_1714 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782 associate-*r*_binary64_1723
Counts
4 → 176
Calls

8 calls:

83.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
42.0ms
(/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta))))
18.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))
13.0ms
(-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))
0.0ms
(+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta)))

series4.7s (0.4%)

Counts
4 → 79
Calls

4 calls:

2.3s
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.9s
(/.f64 (*.f64 (-.f64 (*.f64 alpha alpha) (*.f64 beta beta)) (-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta))))
354.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (*.f64 (+.f64 (*.f64 beta beta) (*.f64 alpha (+.f64 alpha beta))) (-.f64 alpha beta)))
169.0ms
(-.f64 (pow.f64 beta 3) (pow.f64 alpha 3))
Compiler

Compiled 9933 to 7029 computations (29.2% saved)

simplify135.0ms (0%)

Algorithm
1×egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0639313275

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.3b
(/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
5.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
10.3b
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
18.0b
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))

rewrite2.4s (0.2%)

Algorithm
1×rewrite-expression-head
Rules
7253×times-frac_binary64_1789
5426×sqrt-prod_binary64_1799
3545×*-un-lft-identity_binary64_1783
2995×add-sqr-sqrt_binary64_1805
2836×add-cube-cbrt_binary64_1818
2363×associate-*r*_binary64_1723
554×associate-/r/_binary64_1729
346×distribute-lft-out_binary64_1734
287×div-inv_binary64_1780
272×flip-+_binary64_1757 flip3-+_binary64_1786
47×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
37×unswap-sqr_binary64_1751
25×associate-/r*_binary64_1727 sqrt-div_binary64_1800
18×cbrt-undiv_binary64_1817 div-exp_binary64_1834
13×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l*_binary64_1724
10×associate-/l/_binary64_1730
8×associate-/l*_binary64_1728
6×add-log-exp_binary64_1822 pow1_binary64_1844
5×frac-times_binary64_1793
3×flip3--_binary64_1787 associate-*r/_binary64_1725 associate-*l/_binary64_1726 flip--_binary64_1758
2×frac-2neg_binary64_1794 clear-num_binary64_1782
1×+-commutative_binary64_1713 sqrt-undiv_binary64_1804 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854
Counts
4 → 1000
Calls

8 calls:

873.0ms
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
203.0ms
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
24.0ms
(/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
17.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series3.5s (0.3%)

Counts
4 → 80
Calls

4 calls:

1.9s
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
825.0ms
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
543.0ms
(/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
205.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 10814 to 8257 computations (23.6% saved)

simplify660.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1080 → 1080
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0515786928

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 alpha beta) (*.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
13.3b
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
13.3b
(cbrt.f64 (/.f64 (/.f64 (*.f64 (/.f64 (+.f64 alpha beta) (*.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite140.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
126×times-frac_binary64_1789
108×cbrt-prod_binary64_1814
93×*-un-lft-identity_binary64_1783
51×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818
24×associate-/r/_binary64_1729
21×distribute-lft-out_binary64_1734
18×flip-+_binary64_1757 flip3-+_binary64_1786
16×associate-/l/_binary64_1730
14×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
12×div-inv_binary64_1780
10×cbrt-div_binary64_1815
8×frac-times_binary64_1793
6×flip3--_binary64_1787 associate-/r*_binary64_1727 flip--_binary64_1758
4×associate-*r/_binary64_1725 associate-*l/_binary64_1726 cbrt-undiv_binary64_1817 div-exp_binary64_1834 add-log-exp_binary64_1822 pow1_binary64_1844
2×associate-/l*_binary64_1728 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 frac-2neg_binary64_1794 pow1/3_binary64_1865 clear-num_binary64_1782
Counts
4 → 176
Calls

8 calls:

42.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (/.f64 (+.f64 alpha beta) (*.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
19.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series2.5s (0.2%)

Counts
4 → 60
Calls

4 calls:

1.0s
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
998.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (/.f64 (+.f64 alpha beta) (*.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
247.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
228.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 12516 to 7970 computations (36.3% saved)

simplify144.0ms (0%)

Algorithm
1×egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0497112463
1497112463

prune3.6min (19.5%)

Pruning

1405 alts after pruning (1397 fresh and 8 done)

PrunedKeptTotal
New17289322660
Fresh78465543
Picked000
Done2810
Total180814053213
Error
0.1b
Counts
3213 → 1405
Compiler

Compiled 227981 to 137816 computations (39.5% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

3.0b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.4b
(/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.1b
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.4b
(/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.0b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
4.0b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite2.3s (0.2%)

Algorithm
1×rewrite-expression-head
Rules
13777×times-frac_binary64_1789
8053×*-un-lft-identity_binary64_1783
6119×add-sqr-sqrt_binary64_1805
5009×add-cube-cbrt_binary64_1818
1963×associate-*r*_binary64_1723
1611×cbrt-prod_binary64_1814
967×distribute-lft-out_binary64_1734
628×add-exp-log_binary64_1821
555×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
418×associate-/r/_binary64_1729
412×div-inv_binary64_1780
325×div-exp_binary64_1834
234×prod-exp_binary64_1832
191×flip-+_binary64_1757 flip3-+_binary64_1786
159×add-cbrt-cube_binary64_1819
110×associate-/r*_binary64_1727
92×cbrt-undiv_binary64_1817
56×cbrt-unprod_binary64_1816
53×1-exp_binary64_1827 rec-exp_binary64_1833
26×associate-/l*_binary64_1728
10×associate-*l/_binary64_1726 frac-times_binary64_1793
9×pow1_binary64_1844
6×add-log-exp_binary64_1822
3×associate-*r/_binary64_1725 associate-/l/_binary64_1730 pow-prod-down_binary64_1854
2×un-div-inv_binary64_1781 frac-2neg_binary64_1794 clear-num_binary64_1782
1×+-commutative_binary64_1713 associate-*l*_binary64_1724 *-commutative_binary64_1714 sum-log_binary64_1874
Counts
4 → 1000
Calls

8 calls:

404.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
172.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
83.0ms
(/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
20.0ms
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series3.9s (0.4%)

Counts
4 → 89
Calls

4 calls:

1.9s
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
820.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 1 (*.f64 (cbrt.f64 1) (cbrt.f64 1)))) (/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
704.0ms
(/.f64 (/.f64 1 (cbrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
488.0ms
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 11457 to 8881 computations (22.5% saved)

simplify528.0ms (0%)

Algorithm
1×egg-herbie
Counts
1089 → 1089
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0539472418

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
0.1b
(/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.6b
(*.f64 (*.f64 (+.f64 alpha beta) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
3.5b
(sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
3.5b
(sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite3.9s (0.3%)

Algorithm
1×rewrite-expression-head
Rules
28056×times-frac_binary64_1789
16207×*-un-lft-identity_binary64_1783
14154×sqrt-prod_binary64_1799
12325×add-sqr-sqrt_binary64_1805
10363×add-cube-cbrt_binary64_1818
4045×associate-*r*_binary64_1723
1944×distribute-lft-out_binary64_1734
978×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
735×associate-/r/_binary64_1729
612×div-inv_binary64_1780
330×flip-+_binary64_1757 flip3-+_binary64_1786
101×associate-/r*_binary64_1727
89×sqrt-div_binary64_1800
57×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
40×associate-/l*_binary64_1728
24×cbrt-undiv_binary64_1817 div-exp_binary64_1834
15×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
11×pow1_binary64_1844
9×associate-*l/_binary64_1726 frac-times_binary64_1793
4×rem-sqrt-square_binary64_1796 add-log-exp_binary64_1822
3×associate-*r/_binary64_1725 pow-prod-down_binary64_1854
2×pow1/2_binary64_1863 sqrt-pow1_binary64_1801
1×associate-/l/_binary64_1730 associate-*l*_binary64_1724 *-commutative_binary64_1714 frac-2neg_binary64_1794 clear-num_binary64_1782
Counts
4 → 1000
Calls

8 calls:

767.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
147.0ms
(/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
10.0ms
(sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
10.0ms
(sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)

series1.7s (0.2%)

Counts
4 → 62
Calls

4 calls:

828.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
480.0ms
(/.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 1)) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
190.0ms
(sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
189.0ms
(sqrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 7516 to 5591 computations (25.6% saved)

simplify549.0ms (0%)

Algorithm
1×egg-herbie
Counts
1062 → 1062
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0500966629

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (/.f64 (sqrt.f64 (/.f64 1 1)) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
0.0b
(sqrt.f64 (-.f64 beta alpha))
0.0b
(sqrt.f64 (-.f64 beta alpha))
0.1b
(/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (+.f64 alpha beta) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b
(/.f64 (sqrt.f64 (/.f64 1 1)) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))

rewrite4.0s (0.4%)

Algorithm
1×rewrite-expression-head
Rules
26920×times-frac_binary64_1789
18184×sqrt-prod_binary64_1799
15408×*-un-lft-identity_binary64_1783
12264×add-sqr-sqrt_binary64_1805
10388×add-cube-cbrt_binary64_1818
1572×distribute-lft-out_binary64_1734
938×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
778×associate-/r*_binary64_1727
564×div-inv_binary64_1780
336×associate-/r/_binary64_1729
317×sqrt-div_binary64_1800
157×flip-+_binary64_1757 flip3-+_binary64_1786
36×associate-/l*_binary64_1728
26×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
14×cbrt-undiv_binary64_1817 div-exp_binary64_1834
7×associate-/l/_binary64_1730
5×sqrt-undiv_binary64_1804
4×frac-2neg_binary64_1794 clear-num_binary64_1782 add-log-exp_binary64_1822 pow1_binary64_1844
2×flip3--_binary64_1787 flip--_binary64_1758
Counts
4 → 1000
Calls

8 calls:

222.0ms
(/.f64 (sqrt.f64 (/.f64 1 1)) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
116.0ms
(/.f64 (+.f64 alpha beta) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
13.0ms
(/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
13.0ms
(/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0ms
(sqrt.f64 (-.f64 beta alpha))

series2.3s (0.2%)

Counts
4 → 44
Calls

4 calls:

1.2s
(/.f64 (+.f64 alpha beta) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
751.0ms
(/.f64 (sqrt.f64 (/.f64 1 1)) (/.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
201.0ms
(/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
194.0ms
(/.f64 (sqrt.f64 (-.f64 beta alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 8741 to 6153 computations (29.6% saved)

simplify741.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1044 → 1044
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0528387190

localize63.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
0.0b
(-.f64 (+.f64 alpha beta) (*.f64 2 i))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
13.3b
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
14.3b
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i (*.f64 i 4)))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
20.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
23.9b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i (*.f64 i 4))))

rewrite149.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
66×times-frac_binary64_1789
63×cbrt-prod_binary64_1814
47×*-un-lft-identity_binary64_1783
29×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818
24×associate-/r/_binary64_1729
18×flip-+_binary64_1757 flip3-+_binary64_1786
16×associate-/l/_binary64_1730
14×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 cbrt-div_binary64_1815
12×frac-times_binary64_1793
9×distribute-lft-out_binary64_1734 div-inv_binary64_1780
8×flip3--_binary64_1787 flip--_binary64_1758
6×associate-*r/_binary64_1725 associate-/r*_binary64_1727 associate-*l/_binary64_1726
4×cbrt-undiv_binary64_1817 div-exp_binary64_1834 add-log-exp_binary64_1822 pow1_binary64_1844
2×associate-/l*_binary64_1728 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 frac-2neg_binary64_1794 pow1/3_binary64_1865 clear-num_binary64_1782
Counts
4 → 143
Calls

8 calls:

33.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i (*.f64 i 4)))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
20.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
20.0ms
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
20.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i (*.f64 i 4))))
0.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series4.3s (0.4%)

Counts
4 → 55
Calls

4 calls:

2.8s
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i (*.f64 i 4)))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
1.0s
(cbrt.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
263.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
258.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i (*.f64 i 4))))
Compiler

Compiled 16380 to 10628 computations (35.1% saved)

simplify114.0ms (0%)

Algorithm
1×egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0505610327

prune9.7min (52.7%)

Pruning

2263 alts after pruning (2251 fresh and 12 done)

PrunedKeptTotal
New24759183393
Fresh5913331392
Picked000
Done11213
Total253522634798
Error
0.1b
Counts
4798 → 2263
Compiler

Compiled 145391 to 86412 computations (40.6% saved)

simplify8.0s (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
019799480861

regimes3.1min (16.9%)

Compiler

Compiled 2144832 to 1394645 computations (35% saved)

bsearch449.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes3.5s (0.3%)

Compiler

Compiled 42929 to 29137 computations (32.1% saved)

bsearch14.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes1.6s (0.1%)

Compiler

Compiled 14898 to 11819 computations (20.7% saved)

bsearch5.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes821.0ms (0.1%)

Compiler

Compiled 5660 to 4799 computations (15.2% saved)

bsearch32.0ms (0%)

Steps
ItersRangePoint
8
4.013946984393911e+44
6.418987753968373e+47
3.2424984140172976e+45
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes732.0ms (0.1%)

Compiler

Compiled 4855 to 4194 computations (13.6% saved)

bsearch37.0ms (0%)

Steps
ItersRangePoint
10
1.2199827126663331e+27
9.744345353621753e+36
1.6015243294856198e+34
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes226.0ms (0%)

Compiler

Compiled 804 to 821 computations (-2.1% saved)

bsearch31.0ms (0%)

Steps
ItersRangePoint
8
4.013946984393911e+44
6.418987753968373e+47
2.949902580252124e+47
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes127.0ms (0%)

Compiler

Compiled 237 to 282 computations (-19% saved)

bsearch33.0ms (0%)

Steps
ItersRangePoint
11
1.318983615800409e-08
8800483915618.742
22846195777.341858
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes100.0ms (0%)

Compiler

Compiled 159 to 207 computations (-30.2% saved)

bsearch25.0ms (0%)

Steps
ItersRangePoint
9
1.902292553520572e+16
2.659830190167297e+23
7.295694539430045e+19
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes52.0ms (0%)

Compiler

Compiled 120 to 168 computations (-40% saved)

bsearch28.0ms (0%)

Steps
ItersRangePoint
10
195747728899.64023
3.5537220663345458e+28
214997879345.9953
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes24.0ms (0%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch17.0ms (0%)

Compiler

Compiled 431 to 301 computations (30.2% saved)

simplify12.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0315637
1315637

end0.0ms (0%)

sample6.2s (0.6%)

Algorithm
1×intervals
Results
367.0ms6439×body128valid
182.0ms8000×pre128true
147.0ms643×body1024valid
97.0ms567×body512valid
33.0ms303×body256valid
14.0ms48×body2048valid
Compiler

Compiled 276233 to 179358 computations (35.1% saved)

Profiling

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