Details

Time bar (total: 8.6min)

analyze130.0ms (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)

sample46.0ms (0%)

Algorithm
1×intervals
Results
12.0ms196×body128valid
9.0ms256×pre128true
8.0ms33×body1024valid
3.0ms16×body512valid
1.0ms9×body256valid
1.0ms2×body2048valid
Compiler

Compiled 71 to 56 computations (21.1% saved)

simplify164.0ms (0%)

Algorithm
1×egg-herbie
Counts
3 → 3
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
0537145

prune3.0ms (0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New123
Fresh033
Picked000
Done000
Total156
Error
16.5b
Counts
6 → 3
Compiler

Compiled 31 to 22 computations (29% saved)

localize18.0ms (0%)

Local error

Found 6 expressions with local error:

23.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
1.5b
(+.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)
0.1b
(/.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))
0.1b
(/.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))
1.5b
(+.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)
23.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite90.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
54×times-frac_binary64_1789
47×*-un-lft-identity_binary64_1783
25×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818
17×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
14×associate-/r/_binary64_1729
11×distribute-lft-out_binary64_1734 flip-+_binary64_1757 flip3-+_binary64_1786
10×associate-/l*_binary64_1728
9×associate-/l/_binary64_1730
7×div-inv_binary64_1780 associate-/r*_binary64_1727 cbrt-undiv_binary64_1817 div-exp_binary64_1834
5×add-log-exp_binary64_1822
4×frac-times_binary64_1793
3×flip3--_binary64_1787 flip--_binary64_1758 pow1_binary64_1844
2×associate-*r/_binary64_1725 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l/_binary64_1726 frac-2neg_binary64_1794 clear-num_binary64_1782
1×+-commutative_binary64_1713 sum-log_binary64_1874
Counts
3 → 111
Calls

6 calls:

36.0ms
(+.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)
22.0ms
(/.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))
16.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(/.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))
0.0ms
(+.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)

series3.5s (0.7%)

Counts
3 → 75
Calls

3 calls:

1.9s
(+.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)
1.3s
(/.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))
230.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 9242 to 7247 computations (21.6% saved)

simplify137.0ms (0%)

Algorithm
1×egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0587114199

prune1.7s (0.3%)

Pruning

109 alts after pruning (108 fresh and 1 done)

PrunedKeptTotal
New80106186
Fresh022
Picked000
Done011
Total80109189
Error
0.2b
Counts
189 → 109
Compiler

Compiled 15700 to 9614 computations (38.8% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

3.4b
(+.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)
1.8b
(*.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))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(/.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))))
1.8b
(*.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)))))
3.4b
(+.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)

rewrite162.0ms (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:

46.0ms
(*.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)))))
31.0ms
(+.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)
21.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
16.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series4.9s (1%)

Counts
4 → 109
Calls

4 calls:

2.0s
(+.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)
1.4s
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.3s
(*.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)))))
274.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 13765 to 10671 computations (22.5% saved)

simplify281.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
404 → 404
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
0497527146
1497527146

localize2.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.0b
(-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta)))))
0.0b
(*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta)))
0.0b
(*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))
0.1b
(/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
5.2b
(+.f64 (/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
7.7b
(/.f64 (*.f64 alpha i) (+.f64 alpha beta))
9.8b
(/.f64 (*.f64 beta i) (+.f64 alpha beta))

rewrite74.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
51×*-un-lft-identity_binary64_1783
29×add-sqr-sqrt_binary64_1805
28×times-frac_binary64_1789
19×add-cube-cbrt_binary64_1818
16×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
12×associate-/r*_binary64_1727
11×distribute-lft-out_binary64_1734
8×flip-+_binary64_1757 flip3-+_binary64_1786
7×associate-/l*_binary64_1728
6×associate-/l/_binary64_1730 associate-/r/_binary64_1729 add-log-exp_binary64_1822
5×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735 cbrt-undiv_binary64_1817 div-exp_binary64_1834
4×frac-sub_binary64_1792 pow1_binary64_1844
3×div-inv_binary64_1780 frac-2neg_binary64_1794 clear-num_binary64_1782
2×div-sub_binary64_1788 cbrt-unprod_binary64_1816 prod-exp_binary64_1832
1×flip3--_binary64_1787 +-commutative_binary64_1713 associate-+l-_binary64_1718 sum-log_binary64_1874 flip--_binary64_1758
Counts
4 → 113
Calls

8 calls:

23.0ms
(+.f64 (/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
19.0ms
(/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
7.0ms
(/.f64 (*.f64 alpha i) (+.f64 alpha beta))
7.0ms
(/.f64 (*.f64 beta i) (+.f64 alpha beta))
0.0ms
(*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))

series5.3s (1%)

Counts
4 → 80
Calls

4 calls:

4.3s
(+.f64 (/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
774.0ms
(/.f64 (-.f64 (+.f64 beta (*.f64 2 (/.f64 (*.f64 alpha i) (+.f64 alpha beta)))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
107.0ms
(/.f64 (*.f64 beta i) (+.f64 alpha beta))
84.0ms
(/.f64 (*.f64 alpha i) (+.f64 alpha beta))
Compiler

Compiled 10807 to 8164 computations (24.5% saved)

simplify133.0ms (0%)

Algorithm
1×egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0573613125

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
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))))
0.2b
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
9.2b
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite328.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
603×times-frac_binary64_1789
484×*-un-lft-identity_binary64_1783
408×add-sqr-sqrt_binary64_1805
260×add-cube-cbrt_binary64_1818
219×sqrt-prod_binary64_1799
153×associate-*r*_binary64_1723
67×distribute-lft-out_binary64_1734
45×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
38×associate-/r/_binary64_1729
34×associate-*l*_binary64_1724
32×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
25×associate-/l*_binary64_1728
21×flip-+_binary64_1757 flip3-+_binary64_1786
19×div-inv_binary64_1780
15×unswap-sqr_binary64_1751
14×associate-/r*_binary64_1727
13×cbrt-undiv_binary64_1817 div-exp_binary64_1834
8×sqrt-div_binary64_1800
6×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 add-log-exp_binary64_1822 pow1_binary64_1844
3×associate-/l/_binary64_1730
2×div-sub_binary64_1788 frac-2neg_binary64_1794 clear-num_binary64_1782
1×associate-*r/_binary64_1725 +-commutative_binary64_1713 associate-*l/_binary64_1726 *-commutative_binary64_1714 sum-log_binary64_1874 frac-times_binary64_1793 pow-prod-down_binary64_1854
Counts
4 → 485
Calls

8 calls:

135.0ms
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
46.0ms
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
23.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
13.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.0ms
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series4.3s (0.8%)

Counts
4 → 84
Calls

4 calls:

2.0s
(+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
1.3s
(*.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
764.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
307.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 12160 to 9370 computations (22.9% saved)

simplify365.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
569 → 569
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0503939463

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.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))))
0.1b
(/.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))))
0.1b
(*.f64 (cbrt.f64 (+.f64 1 (/.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)))))) (cbrt.f64 (+.f64 1 (/.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 (cbrt.f64 (+.f64 1 (/.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)))))) (cbrt.f64 (+.f64 1 (/.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))))))) (cbrt.f64 (+.f64 1 (/.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)))))))
1.5b
(+.f64 1 (/.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)))))
23.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
23.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
23.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite103.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
24×associate-/l/_binary64_1730
19×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
13×flip-+_binary64_1757 flip3-+_binary64_1786
12×*-un-lft-identity_binary64_1783 frac-times_binary64_1793
10×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818
9×flip3--_binary64_1787 associate-/r*_binary64_1727 times-frac_binary64_1789 flip--_binary64_1758
6×associate-*r/_binary64_1725 associate-/r/_binary64_1729 associate-*l/_binary64_1726 cbrt-undiv_binary64_1817 div-exp_binary64_1834 add-log-exp_binary64_1822
4×pow1_binary64_1844
3×associate-/l*_binary64_1728 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 div-inv_binary64_1780 frac-2neg_binary64_1794 clear-num_binary64_1782
1×+-commutative_binary64_1713 distribute-lft-out_binary64_1734 sum-log_binary64_1874
Counts
4 → 105
Calls

8 calls:

25.0ms
(+.f64 1 (/.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)))))
21.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
16.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
16.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(*.f64 (*.f64 (cbrt.f64 (+.f64 1 (/.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)))))) (cbrt.f64 (+.f64 1 (/.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))))))) (cbrt.f64 (+.f64 1 (/.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)))))))

series2.8s (0.5%)

Counts
4 → 86
Calls

4 calls:

2.0s
(+.f64 1 (/.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)))))
270.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
266.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
257.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 15156 to 10057 computations (33.6% saved)

simplify85.0ms (0%)

Algorithm
1×egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
050647666

prune46.0s (8.9%)

Pruning

615 alts after pruning (611 fresh and 4 done)

PrunedKeptTotal
New8285291357
Fresh2182103
Picked000
Done246
Total8516151466
Error
0.2b
Counts
1466 → 615
Compiler

Compiled 110520 to 65174 computations (41% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.4b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite112.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
54×*-un-lft-identity_binary64_1783
51×add-sqr-sqrt_binary64_1805
50×add-exp-log_binary64_1821
43×times-frac_binary64_1789
39×associate-*r*_binary64_1723
32×add-cbrt-cube_binary64_1819 add-cube-cbrt_binary64_1818
22×prod-exp_binary64_1832
12×cbrt-unprod_binary64_1816 div-exp_binary64_1834
11×associate-*l/_binary64_1726 frac-times_binary64_1793 pow1_binary64_1844
10×flip-+_binary64_1757 flip3-+_binary64_1786
7×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735 cbrt-undiv_binary64_1817
6×associate-/r/_binary64_1729 add-log-exp_binary64_1822
5×associate-/l*_binary64_1728 associate-*l*_binary64_1724
4×associate-*r/_binary64_1725 distribute-lft-out_binary64_1734 pow-prod-down_binary64_1854
3×1-exp_binary64_1827 div-inv_binary64_1780 associate-/r*_binary64_1727 rec-exp_binary64_1833
2×associate-/l/_binary64_1730 *-commutative_binary64_1714 unswap-sqr_binary64_1751
1×flip3--_binary64_1787 div-sub_binary64_1788 un-div-inv_binary64_1781 +-commutative_binary64_1713 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782 flip--_binary64_1758
Counts
4 → 155
Calls

8 calls:

31.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
29.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
19.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
12.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series3.7s (0.7%)

Counts
4 → 102
Calls

4 calls:

1.9s
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
1.3s
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
282.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
231.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 11215 to 8746 computations (22% saved)

simplify178.0ms (0%)

Algorithm
1×egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0496815259
1496815259

localize5.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (+.f64 beta (*.f64 2 (*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta)))))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta)))))
0.0b
(*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta)))
0.0b
(+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))
0.0b
(*.f64 2 (*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta)))))
5.2b
(+.f64 (/.f64 (-.f64 (+.f64 beta (*.f64 2 (*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta)))))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
9.8b
(/.f64 (*.f64 beta i) (+.f64 alpha beta))
14.5b
(/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3)))
34.0b
(*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta))))

rewrite98.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
47×*-un-lft-identity_binary64_1783
23×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
22×times-frac_binary64_1789
18×distribute-lft-out_binary64_1734
15×associate-*l*_binary64_1724
13×add-sqr-sqrt_binary64_1805 associate-/r*_binary64_1727
12×unpow-prod-down_binary64_1862 cube-prod_binary64_1811
11×add-cube-cbrt_binary64_1818
6×associate-/r/_binary64_1729 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 flip-+_binary64_1757 cbrt-undiv_binary64_1817 div-exp_binary64_1834 flip3-+_binary64_1786 add-log-exp_binary64_1822 pow1_binary64_1844
3×sum-cubes_binary64_1784 div-inv_binary64_1780 associate-*r*_binary64_1723
2×associate-*r/_binary64_1725 associate-/l*_binary64_1728 frac-2neg_binary64_1794 frac-times_binary64_1793 clear-num_binary64_1782
1×div-sub_binary64_1788 +-commutative_binary64_1713 distribute-lft-in_binary64_1732 associate-+l-_binary64_1718 associate-*l/_binary64_1726 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 sum-log_binary64_1874 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
Counts
4 → 114
Calls

8 calls:

27.0ms
(*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta))))
25.0ms
(+.f64 (/.f64 (-.f64 (+.f64 beta (*.f64 2 (*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta)))))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
19.0ms
(/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3)))
7.0ms
(/.f64 (*.f64 beta i) (+.f64 alpha beta))
0.0ms
(*.f64 2 (*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta)))))

series11.0s (2.1%)

Counts
4 → 61
Calls

4 calls:

10.4s
(+.f64 (/.f64 (-.f64 (+.f64 beta (*.f64 2 (*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta)))))) (+.f64 alpha (*.f64 2 (/.f64 (*.f64 beta i) (+.f64 alpha beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
246.0ms
(*.f64 (/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (*.f64 alpha alpha) (-.f64 (*.f64 beta beta) (*.f64 alpha beta))))
188.0ms
(/.f64 (*.f64 i alpha) (+.f64 (pow.f64 beta 3) (pow.f64 alpha 3)))
135.0ms
(/.f64 (*.f64 beta i) (+.f64 alpha beta))
Compiler

Compiled 10655 to 8122 computations (23.8% saved)

simplify99.0ms (0%)

Algorithm
1×egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
051258915

localize21.0ms (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
(sqrt.f64 (+.f64 alpha beta))
0.0b
(sqrt.f64 (+.f64 alpha beta))
0.1b
(/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
1.0b
(*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
3.2b
(+.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)

rewrite253.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
358×times-frac_binary64_1789
315×*-un-lft-identity_binary64_1783
227×add-sqr-sqrt_binary64_1805
197×sqrt-prod_binary64_1799
179×add-cube-cbrt_binary64_1818
76×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
46×associate-*l*_binary64_1724
44×distribute-lft-out_binary64_1734
29×cbrt-undiv_binary64_1817 div-exp_binary64_1834
28×associate-/l*_binary64_1728
26×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
24×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
20×associate-/r/_binary64_1729
14×associate-/r*_binary64_1727
12×flip-+_binary64_1757 flip3-+_binary64_1786
11×div-inv_binary64_1780
9×pow1_binary64_1844
6×sqrt-div_binary64_1800 add-log-exp_binary64_1822
5×associate-*r/_binary64_1725 frac-times_binary64_1793
3×associate-/l/_binary64_1730 associate-*l/_binary64_1726 pow-prod-down_binary64_1854
2×div-sub_binary64_1788 frac-2neg_binary64_1794 clear-num_binary64_1782
1×+-commutative_binary64_1713 sqrt-undiv_binary64_1804 *-commutative_binary64_1714 sum-log_binary64_1874 associate-*r*_binary64_1723
Counts
4 → 376
Calls

8 calls:

60.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
59.0ms
(+.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
27.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
14.0ms
(/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.0ms
(sqrt.f64 (+.f64 alpha beta))

series4.4s (0.8%)

Counts
4 → 90
Calls

4 calls:

2.0s
(+.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
1.3s
(*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
753.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
364.0ms
(/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 13182 to 10031 computations (23.9% saved)

simplify306.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0500633103

localize54.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3))) (/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i)))))
0.0b
(/.f64 alpha (+.f64 beta (*.f64 2 i)))
0.0b
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 i) (+.f64 beta 2)))) (/.f64 beta (+.f64 beta (*.f64 2 i)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 i) (+.f64 beta 2)))) (/.f64 alpha (+.f64 beta (*.f64 2 i)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 i) (+.f64 beta 2)))) (/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 beta (*.f64 2 i)) 2))) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3))) (/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i))))))))
1.2b
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3))) (/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i))))
8.2b
(/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i)))
12.3b
(/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 beta (*.f64 2 i)) 2))
15.3b
(sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3)))

rewrite133.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
102×times-frac_binary64_1789
93×sqrt-prod_binary64_1799
90×add-sqr-sqrt_binary64_1805
65×*-un-lft-identity_binary64_1783
57×add-cube-cbrt_binary64_1818
45×associate-*l*_binary64_1724
31×add-exp-log_binary64_1821
28×unpow-prod-down_binary64_1862
23×add-cbrt-cube_binary64_1819
22×cube-prod_binary64_1811
12×sqr-pow_binary64_1755
11×associate-/r*_binary64_1727
10×div-exp_binary64_1834 unswap-sqr_binary64_1751
9×rem-sqrt-square_binary64_1796 associate-*r*_binary64_1723
8×associate-/r/_binary64_1729 prod-exp_binary64_1832
7×pow1_binary64_1844
6×cube-mult_binary64_1813 cbrt-unprod_binary64_1816 unpow3_binary64_1849 cbrt-undiv_binary64_1817
5×div-inv_binary64_1780
4×flip-+_binary64_1757 flip3-+_binary64_1786 cube-div_binary64_1812 add-log-exp_binary64_1822
3×sqrt-div_binary64_1800 sqrt-pow1_binary64_1801
2×associate-/l*_binary64_1728 unpow2_binary64_1848 frac-2neg_binary64_1794 clear-num_binary64_1782 pow-to-exp_binary64_1852 pow-exp_binary64_1851
1×associate-*r/_binary64_1725 inv-pow_binary64_1868 pow-flip_binary64_1857 pow1/2_binary64_1863 associate-*l/_binary64_1726 *-commutative_binary64_1714 frac-times_binary64_1793 pow-prod-down_binary64_1854
Counts
4 → 203
Calls

8 calls:

39.0ms
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3))) (/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i))))
13.0ms
(sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3)))
8.0ms
(/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 beta (*.f64 2 i)) 2))
7.0ms
(/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i)))
0.0ms
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 i) (+.f64 beta 2)))) (/.f64 beta (+.f64 beta (*.f64 2 i)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 i) (+.f64 beta 2)))) (/.f64 alpha (+.f64 beta (*.f64 2 i)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 i) (+.f64 beta 2)))) (/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 beta (*.f64 2 i)) 2))) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3))) (/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i))))))))

series2.6s (0.5%)

Counts
4 → 51
Calls

4 calls:

1.1s
(sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3)))
1.0s
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (*.f64 2 i) (+.f64 beta 2)) 3))) (/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i))))
269.0ms
(/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 beta (*.f64 2 i)) 2))
206.0ms
(/.f64 (*.f64 alpha beta) (+.f64 beta (*.f64 2 i)))
Compiler

Compiled 12275 to 9496 computations (22.6% saved)

simplify107.0ms (0%)

Algorithm
1×egg-herbie
Counts
254 → 254
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
050449782

prune1.4min (16.3%)

Pruning

968 alts after pruning (963 fresh and 5 done)

PrunedKeptTotal
New7543981152
Fresh41565606
Picked000
Done459
Total7999681767
Error
0.1b
Counts
1767 → 968
Compiler

Compiled 136000 to 87437 computations (35.7% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.4b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite121.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
67×*-un-lft-identity_binary64_1783
58×add-sqr-sqrt_binary64_1805
55×times-frac_binary64_1789
51×associate-*r*_binary64_1723
39×add-cube-cbrt_binary64_1818
32×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
12×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 sqrt-prod_binary64_1799
11×associate-*l/_binary64_1726 frac-times_binary64_1793 pow1_binary64_1844
10×flip-+_binary64_1757 flip3-+_binary64_1786
7×difference-of-squares_binary64_1752 distribute-lft-out_binary64_1734 distribute-lft-out--_binary64_1735 cbrt-undiv_binary64_1817 div-exp_binary64_1834
6×associate-/r/_binary64_1729 add-log-exp_binary64_1822
5×associate-/l*_binary64_1728 associate-*l*_binary64_1724
4×associate-*r/_binary64_1725 pow-prod-down_binary64_1854
3×div-inv_binary64_1780 associate-/r*_binary64_1727
2×associate-/l/_binary64_1730 *-commutative_binary64_1714 unswap-sqr_binary64_1751
1×flip3--_binary64_1787 div-sub_binary64_1788 +-commutative_binary64_1713 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782 flip--_binary64_1758
Counts
4 → 160
Calls

8 calls:

33.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
30.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
24.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
11.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0ms
(/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series3.8s (0.7%)

Counts
4 → 102
Calls

4 calls:

2.0s
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
1.3s
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (/.f64 (sqrt.f64 1) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
285.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
233.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 11278 to 8809 computations (21.9% saved)

simplify178.0ms (0%)

Algorithm
1×egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0496815497
1496815497

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

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
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))))
0.2b
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.4b
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b
(/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
9.2b
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite179.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
116×sqrt-prod_binary64_1799
104×times-frac_binary64_1789
102×*-un-lft-identity_binary64_1783
86×add-sqr-sqrt_binary64_1805
68×add-cube-cbrt_binary64_1818
48×associate-*r*_binary64_1723
47×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
17×cbrt-undiv_binary64_1817 div-exp_binary64_1834
16×distribute-lft-out_binary64_1734
14×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-/r*_binary64_1727
13×associate-*l*_binary64_1724
8×associate-/r/_binary64_1729 sqrt-div_binary64_1800
7×associate-/l*_binary64_1728 flip-+_binary64_1757 flip3-+_binary64_1786 unswap-sqr_binary64_1751
6×add-log-exp_binary64_1822 pow1_binary64_1844
5×associate-/l/_binary64_1730
4×div-inv_binary64_1780
3×associate-*l/_binary64_1726 frac-times_binary64_1793
2×associate-*r/_binary64_1725 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 → 215
Calls

8 calls:

58.0ms
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
38.0ms
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
24.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
12.0ms
(/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.0ms
(sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series4.2s (0.8%)

Counts
4 → 84
Calls

4 calls:

2.0s
(+.f64 (*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
1.3s
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
697.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
191.0ms
(/.f64 (sqrt.f64 1) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 11650 to 9081 computations (22.1% saved)

simplify217.0ms (0%)

Algorithm
1×egg-herbie
Counts
299 → 299
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0496920063
1496920063

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (sqrt.f64 beta) (sqrt.f64 alpha))
0.0b
(sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b
(+.f64 (sqrt.f64 beta) (sqrt.f64 alpha))
0.1b
(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
1.7b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite324.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
542×times-frac_binary64_1789
480×*-un-lft-identity_binary64_1783
466×add-sqr-sqrt_binary64_1805
352×sqrt-prod_binary64_1799
282×associate-*r*_binary64_1723
210×add-cube-cbrt_binary64_1818
124×difference-of-squares_binary64_1752
73×distribute-lft-out_binary64_1734
62×distribute-lft-out--_binary64_1735
47×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
17×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
14×associate-/r/_binary64_1729 flip-+_binary64_1757 cbrt-undiv_binary64_1817 div-exp_binary64_1834 flip3-+_binary64_1786
12×sqrt-div_binary64_1800
11×associate-*l/_binary64_1726 frac-times_binary64_1793 pow1_binary64_1844
9×associate-/l*_binary64_1728
7×div-inv_binary64_1780
6×associate-/r*_binary64_1727 add-log-exp_binary64_1822
5×associate-*l*_binary64_1724
4×associate-*r/_binary64_1725 pow-prod-down_binary64_1854
3×unswap-sqr_binary64_1751
2×associate-/l/_binary64_1730 *-commutative_binary64_1714
1×flip3--_binary64_1787 div-sub_binary64_1788 +-commutative_binary64_1713 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782 flip--_binary64_1758
Counts
4 → 444
Calls

8 calls:

94.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
60.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
34.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
17.0ms
(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.0ms
(+.f64 (sqrt.f64 beta) (sqrt.f64 alpha))

series3.8s (0.7%)

Counts
4 → 57
Calls

4 calls:

1.8s
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
1.4s
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
285.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
232.0ms
(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
Compiler

Compiled 10076 to 7537 computations (25.2% saved)

simplify320.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
501 → 501
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
0496830861
1496830861

localize52.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 1/2 (*.f64 (/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3)))))
0.0b
(/.f64 beta (+.f64 alpha (*.f64 2 i)))
0.0b
(sqrt.f64 (+.f64 alpha beta))
0.0b
(sqrt.f64 (+.f64 alpha beta))
6.3b
(+.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (-.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3))))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 2 (*.f64 2 i))))) (+.f64 (/.f64 beta (+.f64 alpha (*.f64 2 i))) (/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 alpha (*.f64 2 i)) 2))))) (*.f64 (/.f64 alpha (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 2 (*.f64 2 i))))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
8.2b
(/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i)))
12.5b
(/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 alpha (*.f64 2 i)) 2))
13.9b
(sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3)))

rewrite172.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
61×times-frac_binary64_1789
50×*-un-lft-identity_binary64_1783
48×sqrt-prod_binary64_1799
45×add-sqr-sqrt_binary64_1805
34×add-cube-cbrt_binary64_1818
22×add-exp-log_binary64_1821
20×unpow-prod-down_binary64_1862
14×add-cbrt-cube_binary64_1819 cube-prod_binary64_1811
11×associate-/r*_binary64_1727
9×rem-sqrt-square_binary64_1796
8×div-exp_binary64_1834
7×sqr-pow_binary64_1755
6×distribute-lft-out_binary64_1734 add-log-exp_binary64_1822
5×pow1_binary64_1844
4×associate-/r/_binary64_1729 prod-exp_binary64_1832 cbrt-undiv_binary64_1817
3×cube-mult_binary64_1813 flip-+_binary64_1757 unpow3_binary64_1849 div-inv_binary64_1780 flip3-+_binary64_1786 sqrt-pow1_binary64_1801
2×associate-/l*_binary64_1728 cbrt-unprod_binary64_1816 unpow2_binary64_1848 frac-2neg_binary64_1794 clear-num_binary64_1782 cube-div_binary64_1812 pow-to-exp_binary64_1852 pow-exp_binary64_1851
1×+-commutative_binary64_1713 inv-pow_binary64_1868 pow-flip_binary64_1857 pow1/2_binary64_1863 sqrt-div_binary64_1800 sum-log_binary64_1874
Counts
4 → 138
Calls

8 calls:

105.0ms
(+.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (-.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3))))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 2 (*.f64 2 i))))) (+.f64 (/.f64 beta (+.f64 alpha (*.f64 2 i))) (/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 alpha (*.f64 2 i)) 2))))) (*.f64 (/.f64 alpha (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 2 (*.f64 2 i))))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
13.0ms
(sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3)))
8.0ms
(/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 alpha (*.f64 2 i)) 2))
6.0ms
(/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i)))
0.0ms
(sqrt.f64 (+.f64 alpha beta))

series14.0s (2.7%)

Counts
4 → 39
Calls

4 calls:

13.4s
(+.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 1)) (*.f64 (-.f64 (+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3))))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 2 (*.f64 2 i))))) (+.f64 (/.f64 beta (+.f64 alpha (*.f64 2 i))) (/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 alpha (*.f64 2 i)) 2))))) (*.f64 (/.f64 alpha (+.f64 alpha (*.f64 2 i))) (sqrt.f64 (/.f64 1 (+.f64 alpha (+.f64 2 (*.f64 2 i))))))) (/.f64 (sqrt.f64 (+.f64 alpha beta)) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) 1)
226.0ms
(sqrt.f64 (/.f64 1 (pow.f64 (+.f64 alpha (+.f64 2 (*.f64 2 i))) 3)))
225.0ms
(/.f64 (*.f64 alpha beta) (pow.f64 (+.f64 alpha (*.f64 2 i)) 2))
158.0ms
(/.f64 (*.f64 alpha beta) (+.f64 alpha (*.f64 2 i)))
Compiler

Compiled 11944 to 9020 computations (24.5% saved)

simplify120.0ms (0%)

Algorithm
1×egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049607358
149607358

prune1.8min (20.7%)

Pruning

1303 alts after pruning (1295 fresh and 8 done)

PrunedKeptTotal
New8673721239
Fresh35923958
Picked000
Done2810
Total90413032207
Error
0.1b
Counts
2207 → 1303
Compiler

Compiled 48095 to 28312 computations (41.1% saved)

simplify4.2s (0.8%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
013384253342

regimes1.4min (16.6%)

Compiler

Compiled 1208252 to 804292 computations (33.4% saved)

bsearch245.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes3.4s (0.7%)

Compiler

Compiled 47169 to 33502 computations (29% saved)

bsearch12.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes1.1s (0.2%)

Compiler

Compiled 12700 to 10301 computations (18.9% saved)

bsearch4.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes610.0ms (0.1%)

Compiler

Compiled 5694 to 4848 computations (14.9% saved)

bsearch42.0ms (0%)

Steps
ItersRangePoint
9
8.046098816053247e+115
5.322377487024607e+120
8.169303527528793e+115
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes684.0ms (0.1%)

Compiler

Compiled 5549 to 4748 computations (14.4% saved)

bsearch37.0ms (0%)

Steps
ItersRangePoint
9
8.046098816053247e+115
5.322377487024607e+120
9.647760065235352e+115
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes206.0ms (0%)

Compiler

Compiled 999 to 997 computations (0.2% saved)

bsearch37.0ms (0%)

Steps
ItersRangePoint
9
8.046098816053247e+115
5.322377487024607e+120
1.7832028453706053e+117
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes181.0ms (0%)

Compiler

Compiled 756 to 781 computations (-3.3% saved)

bsearch23.0ms (0%)

Steps
ItersRangePoint
5
7.231320550363493e+147
2.4450284768884264e+148
7.409244970131082e+147
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes156.0ms (0%)

Compiler

Compiled 467 to 517 computations (-10.7% saved)

bsearch24.0ms (0%)

Steps
ItersRangePoint
5
7.231320550363493e+147
2.4450284768884264e+148
7.409244970131082e+147
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes102.0ms (0%)

Compiler

Compiled 198 to 234 computations (-18.2% saved)

bsearch37.0ms (0%)

Steps
ItersRangePoint
6
5.531427444921846e+97
4.1925343929377414e+98
5.60925540053646e+97
6
365117.9742894661
2624798.035717599
2577959.6744566467
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes99.0ms (0%)

Compiler

Compiled 120 to 159 computations (-32.5% saved)

bsearch25.0ms (0%)

Steps
ItersRangePoint
6
5.531427444921846e+97
4.1925343929377414e+98
5.60925540053646e+97
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes54.0ms (0%)

Compiler

Compiled 81 to 120 computations (-48.1% saved)

bsearch26.0ms (0%)

Steps
ItersRangePoint
8
1.9114035462697245e+65
8.234562105085597e+67
2.0010033081354466e+65
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes21.0ms (0%)

Accuracy

Total 1.3b remaining (97.3%)

Threshold costs 0b (0%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch21.0ms (0%)

Compiler

Compiled 510 to 365 computations (28.4% saved)

simplify13.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0296753
1296753

end0.0ms (0%)

sample1.8min (20.8%)

Algorithm
1×intervals
Results
387.0ms6498×body128valid
189.0ms8000×pre128true
163.0ms667×body1024valid
86.0ms479×body512valid
35.0ms302×body256valid
16.0ms54×body2048valid
Compiler

Compiled 158870 to 105841 computations (33.4% saved)

Pareto

0.7576167359920258

Profiling

Loading profile data...