Details

Time bar (total: 41.4s)

analyze194.0ms (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
12.0ms219×body128valid
6.0ms256×pre128true
3.0ms14×body1024valid
3.0ms15×body512valid
1.0msbody256valid
1.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify180.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
0537143

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 21.9b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize16.0ms (0%)

Local error

Found 3 expressions with local error:

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))
1.4b
(+.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)
19.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite110.0ms (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:

37.0ms
(+.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)
31.0ms
(/.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))
22.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series813.0ms (2%)

Counts
3 → 9
Calls

3 calls:

392.0ms
(+.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)
343.0ms
(/.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))
78.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify127.0ms (0.3%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
049415261
149415261

prune290.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1137120
Fresh000
Picked101
Done000
Total1147121

Merged error: 4.2b

Counts
121 → 7
Compiler

Compiled 5248 to 2745 computations (47.7% saved)

localize18.0ms (0%)

Local error

Found 4 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))))))
0.3b
(/.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)))))
5.5b
(+.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)

rewrite407.0ms (1%)

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:

176.0ms
(*.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))))))
51.0ms
(+.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)
34.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series1.2s (2.9%)

Counts
4 → 12
Calls

4 calls:

421.0ms
(+.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)
389.0ms
(*.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))))))
207.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
175.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify271.0ms (0.7%)

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0541127691

prune2.4s (5.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4925497
Fresh336
Picked101
Done000
Total4968504

Merged error: 4.2b

Counts
504 → 8
Compiler

Compiled 30196 to 16877 computations (44.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.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)))))
2.2b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
6.3b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite1.8s (4.2%)

Algorithm
rewrite-expression-head
Rules
6211×times-frac_binary64_1789
4294×*-un-lft-identity_binary64_1783
3048×add-sqr-sqrt_binary64_1805
2585×sqrt-prod_binary64_1799
2326×add-cube-cbrt_binary64_1818
1077×associate-*r*_binary64_1723
645×distribute-lft-out_binary64_1734
339×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
262×associate-/r/_binary64_1729
174×associate-/l*_binary64_1728
134×flip-+_binary64_1757 flip3-+_binary64_1786
131×div-inv_binary64_1780
36×sqrt-div_binary64_1800
32×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
15×cbrt-undiv_binary64_1817 div-exp_binary64_1834
14×associate-/r*_binary64_1727
11×unswap-sqr_binary64_1751
add-log-exp_binary64_1822 pow1_binary64_1844
div-sub_binary64_1788
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l*_binary64_1724
associate-/l/_binary64_1730 associate-*l/_binary64_1726 frac-2neg_binary64_1794 frac-times_binary64_1793 clear-num_binary64_1782
associate-*r/_binary64_1725 +-commutative_binary64_1713 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854
Counts
4 → 2569
Calls

4 calls:

416.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
143.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
104.0ms
(/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
36.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series1.1s (2.6%)

Counts
4 → 12
Calls

4 calls:

414.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
337.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
177.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
153.0ms
(/.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify1.4s (3.3%)

Algorithm
egg-herbie
Counts
2581 → 2581
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
05569178770

prune25.1s (60.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New257832581
Fresh257
Picked101
Done000
Total258182589

Merged error: 4.2b

Counts
2589 → 8
Compiler

Compiled 179658 to 101872 computations (43.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
2.2b
(*.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)))))
2.4b
(+.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)
2.4b
(log.f64 (exp.f64 (+.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)))

rewrite186.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
306×times-frac_binary64_1789
274×*-un-lft-identity_binary64_1783
195×add-sqr-sqrt_binary64_1805
132×add-cube-cbrt_binary64_1818
90×associate-*r*_binary64_1723
44×distribute-lft-out_binary64_1734
27×difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735
22×associate-/r/_binary64_1729
21×associate-/l*_binary64_1728
18×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
14×flip-+_binary64_1757 flip3-+_binary64_1786
11×div-inv_binary64_1780
pow1_binary64_1844
cbrt-undiv_binary64_1817 div-exp_binary64_1834 add-log-exp_binary64_1822
log-prod_binary64_1869 log-pow_binary64_1872 associate-/r*_binary64_1727 associate-*l*_binary64_1724
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 unswap-sqr_binary64_1751 exp-prod_binary64_1835
div-sub_binary64_1788 associate-*l/_binary64_1726 frac-times_binary64_1793
associate-*r/_binary64_1725 associate-/l/_binary64_1730 +-commutative_binary64_1713 exp-sum_binary64_1829 *-commutative_binary64_1714 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782 pow-prod-down_binary64_1854 rem-log-exp_binary64_1824
Counts
4 → 271
Calls

4 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)))))
32.0ms
(+.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)
30.0ms
(log.f64 (exp.f64 (+.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)))
22.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.4s (3.3%)

Counts
4 → 12
Calls

4 calls:

579.0ms
(log.f64 (exp.f64 (+.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)))
348.0ms
(+.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)
296.0ms
(*.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)))))
154.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify149.0ms (0.4%)

Algorithm
egg-herbie
Counts
283 → 283
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0509513204

prune661.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2830283
Fresh077
Picked011
Done000
Total2838291

Merged error: 4.2b

Counts
291 → 8
Compiler

Compiled 13926 to 7590 computations (45.5% saved)

regimes1.0s (2.5%)

Compiler

Compiled 18470 to 12123 computations (34.4% saved)

bsearch5.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067110
167110

end0.0ms (0%)

sample2.6s (6.4%)

Algorithm
intervals
Results
370.0ms6452×body128valid
188.0ms8000×pre128true
144.0ms648×body1024valid
90.0ms540×body512valid
33.0ms305×body256valid
19.0ms55×body2048valid
Compiler

Compiled 2689 to 1762 computations (34.5% saved)

Profiling

Loading profile data...