Details

Time bar (total: 27.3s)

analyze126.0ms (0.5%)

Algorithm
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)

sample38.0ms (0.1%)

Algorithm
intervals
Results
12.0ms211×body128valid
6.0ms256×pre128true
5.0ms25×body1024valid
2.0ms11×body512valid
1.0msbody256valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify163.0ms (0.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0537143

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 25.0b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))
1.3b
(+.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)
22.2b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite91.0ms (0.3%)

Algorithm
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
associate-/l/_binary64_1730
div-inv_binary64_1780 associate-/r*_binary64_1727 cbrt-undiv_binary64_1817 div-exp_binary64_1834
add-log-exp_binary64_1822
frac-times_binary64_1793
flip3--_binary64_1787 flip--_binary64_1758 pow1_binary64_1844
associate-*r/_binary64_1725 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l/_binary64_1726 frac-2neg_binary64_1794 clear-num_binary64_1782
+-commutative_binary64_1713 sum-log_binary64_1874
Counts
3 → 111
Calls

3 calls:

34.0ms
(+.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))
15.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series2.7s (9.7%)

Counts
3 → 49
Calls

3 calls:

1.5s
(+.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)
1.0s
(/.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))
171.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 6374 to 5005 computations (21.5% saved)

simplify101.0ms (0.4%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0565210291

prune475.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New14515160
Fresh000
Picked101
Done000
Total14615161

Merged error: 10.6b

Counts
161 → 15
Compiler

Compiled 9312 to 5410 computations (41.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(/.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 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.3b
(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite98.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity_binary64_1783
45×add-sqr-sqrt_binary64_1805
35×times-frac_binary64_1789
26×add-cube-cbrt_binary64_1818
21×associate-*r*_binary64_1723
20×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
flip-+_binary64_1757 flip3-+_binary64_1786
associate-/l/_binary64_1730 difference-of-squares_binary64_1752 associate-/r*_binary64_1727 distribute-lft-out--_binary64_1735
associate-/r/_binary64_1729 associate-/l*_binary64_1728 cbrt-undiv_binary64_1817 div-exp_binary64_1834 add-log-exp_binary64_1822 pow1_binary64_1844
distribute-lft-out_binary64_1734 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l*_binary64_1724 associate-*l/_binary64_1726 frac-times_binary64_1793
div-inv_binary64_1780
associate-*r/_binary64_1725 frac-2neg_binary64_1794 clear-num_binary64_1782 unswap-sqr_binary64_1751
flip3--_binary64_1787 div-sub_binary64_1788 +-commutative_binary64_1713 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854 flip--_binary64_1758
Counts
4 → 129
Calls

4 calls:

27.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
25.0ms
(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
18.0ms
(*.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)))

series2.9s (10.5%)

Counts
4 → 66
Calls

4 calls:

1.5s
(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.0s
(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
179.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
175.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
Compiler

Compiled 7495 to 5842 computations (22.1% saved)

simplify120.0ms (0.4%)

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049769733
149769733

prune505.0ms (1.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1923195
Fresh31114
Picked011
Done000
Total19515210

Merged error: 10.6b

Counts
210 → 15
Compiler

Compiled 10231 to 5940 computations (41.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.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)))))
5.7b
(+.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)

rewrite322.0ms (1.2%)

Algorithm
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
sqrt-div_binary64_1800
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 add-log-exp_binary64_1822 pow1_binary64_1844
associate-/l/_binary64_1730
div-sub_binary64_1788 frac-2neg_binary64_1794 clear-num_binary64_1782
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

4 calls:

130.0ms
(*.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))))))
43.0ms
(+.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)
26.0ms
(/.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)))))

series3.4s (12.6%)

Counts
4 → 59
Calls

4 calls:

1.5s
(+.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)
1.0s
(*.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))))))
642.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
273.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 9167 to 7080 computations (22.8% saved)

simplify307.0ms (1.1%)

Algorithm
egg-herbie
Counts
544 → 544
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0501735116

prune2.9s (10.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New5413544
Fresh7613
Picked101
Done011
Total54910559

Merged error: 10.6b

Counts
559 → 10
Compiler

Compiled 35715 to 20671 computations (42.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.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)))))
5.7b
(+.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)

rewrite331.0ms (1.2%)

Algorithm
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
sqrt-div_binary64_1800
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 add-log-exp_binary64_1822 pow1_binary64_1844
associate-/l/_binary64_1730
div-sub_binary64_1788 frac-2neg_binary64_1794 clear-num_binary64_1782
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

4 calls:

128.0ms
(*.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))))))
42.0ms
(+.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)
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 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series3.5s (12.7%)

Counts
4 → 59
Calls

4 calls:

1.5s
(+.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)
1.0s
(*.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))))))
656.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
287.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
Compiler

Compiled 9440 to 7353 computations (22.1% saved)

simplify321.0ms (1.2%)

Algorithm
egg-herbie
Counts
544 → 544
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0501735116

prune3.2s (11.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New5377544
Fresh628
Picked101
Done011
Total54410554

Merged error: 10.6b

Counts
554 → 10
Compiler

Compiled 36914 to 22020 computations (40.3% saved)

regimes1.9s (6.9%)

Compiler

Compiled 30605 to 20727 computations (32.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03243
13243

end0.0ms (0%)

sample3.9s (14.2%)

Algorithm
intervals
Results
374.0ms6506×body128valid
183.0ms8000×pre128true
154.0ms685×body1024valid
77.0ms456×body512valid
33.0ms297×body256valid
18.0ms56×body2048valid
Compiler

Compiled 4375 to 2959 computations (32.4% saved)

Profiling

Loading profile data...