Details

Time bar (total: 18.0s)

analyze126.0ms (0.7%)

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)

sample36.0ms (0.2%)

Algorithm
intervals
Results
12.0ms209×body128valid
6.0ms256×pre128true
4.0ms18×body1024valid
3.0ms16×body512valid
1.0ms11×body256valid
1.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify218.0ms (1.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0506343

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 21.6b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (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))
1.4b
(+.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)
18.0b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite98.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64_1768
47×*-un-lft-identity_binary64_1762
25×add-sqr-sqrt_binary64_1783 add-cube-cbrt_binary64_1794
17×add-cbrt-cube_binary64_1795 add-exp-log_binary64_1797
14×associate-/r/_binary64_1710
11×flip3-+_binary64_1765 flip-+_binary64_1736 distribute-lft-out_binary64_1715
10×associate-/l*_binary64_1709
associate-/l/_binary64_1711
associate-/r*_binary64_1708 div-inv_binary64_1759 cbrt-undiv_binary64_1793 div-exp_binary64_1810
add-log-exp_binary64_1798
frac-times_binary64_1772
flip3--_binary64_1766 flip--_binary64_1737 pow1_binary64_1820
frac-2neg_binary64_1773 prod-exp_binary64_1808 clear-num_binary64_1761 associate-*l/_binary64_1707 associate-*r/_binary64_1706 cbrt-unprod_binary64_1792
+-commutative_binary64_1694 sum-log_binary64_1850
Counts
3 → 111
Calls

3 calls:

38.0ms
(+.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)
28.0ms
(/.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)))

series1.4s (7.6%)

Counts
3 → 9
Calls

3 calls:

676.0ms
(+.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)
576.0ms
(/.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))
119.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify98.0ms (0.5%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049375261
149375261

prune240.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1119120
Fresh000
Picked101
Done000
Total1129121

Merged error: 7.0b

Counts
121 → 9
Compiler

Compiled 5346 to 2803 computations (47.6% saved)

localize15.0ms (0.1%)

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)))))
0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.5b
(+.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)

rewrite345.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
603×times-frac_binary64_1768
484×*-un-lft-identity_binary64_1762
408×add-sqr-sqrt_binary64_1783
260×add-cube-cbrt_binary64_1794
219×sqrt-prod_binary64_1777
153×associate-*r*_binary64_1704
67×distribute-lft-out_binary64_1715
45×distribute-lft-out--_binary64_1716 difference-of-squares_binary64_1731
38×associate-/r/_binary64_1710
34×associate-*l*_binary64_1705
32×add-cbrt-cube_binary64_1795 add-exp-log_binary64_1797
25×associate-/l*_binary64_1709
21×flip3-+_binary64_1765 flip-+_binary64_1736
19×div-inv_binary64_1759
15×unswap-sqr_binary64_1730
14×associate-/r*_binary64_1708
13×cbrt-undiv_binary64_1793 div-exp_binary64_1810
sqrt-div_binary64_1778
prod-exp_binary64_1808 add-log-exp_binary64_1798 cbrt-unprod_binary64_1792 pow1_binary64_1820
associate-/l/_binary64_1711
frac-2neg_binary64_1773 div-sub_binary64_1767 clear-num_binary64_1761
frac-times_binary64_1772 pow-prod-down_binary64_1830 associate-*l/_binary64_1707 +-commutative_binary64_1694 associate-*r/_binary64_1706 *-commutative_binary64_1695 sum-log_binary64_1850
Counts
4 → 485
Calls

4 calls:

134.0ms
(*.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))))))
47.0ms
(+.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)
25.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
16.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series1.9s (10.8%)

Counts
4 → 12
Calls

4 calls:

680.0ms
(+.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)
599.0ms
(*.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))))))
386.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
280.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify256.0ms (1.4%)

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0535327691

prune2.0s (10.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New4934497
Fresh358
Picked011
Done000
Total49610506

Merged error: 7.0b

Counts
506 → 10
Compiler

Compiled 30257 to 16916 computations (44.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (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 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
8.4b
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (*.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 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))) 1)

rewrite209.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
337×times-frac_binary64_1768
301×*-un-lft-identity_binary64_1762
217×add-sqr-sqrt_binary64_1783
187×sqrt-prod_binary64_1777
169×add-cube-cbrt_binary64_1794
42×distribute-lft-out_binary64_1715
28×associate-/l*_binary64_1709
27×associate-/r*_binary64_1708
24×distribute-lft-out--_binary64_1716 difference-of-squares_binary64_1731
22×associate-/r/_binary64_1710
15×add-exp-log_binary64_1797
13×flip3-+_binary64_1765 flip-+_binary64_1736 add-cbrt-cube_binary64_1795
11×div-inv_binary64_1759
10×sqrt-div_binary64_1778
pow1_binary64_1820
add-log-exp_binary64_1798 div-exp_binary64_1810
pow-flip_binary64_1833 cbrt-undiv_binary64_1793
sqrt-pow1_binary64_1779
frac-2neg_binary64_1773 associate-/l/_binary64_1711 clear-num_binary64_1761
div-sub_binary64_1767 pow1/2_binary64_1839
inv-pow_binary64_1844 +-commutative_binary64_1694 1-exp_binary64_1803 rec-exp_binary64_1809 sum-log_binary64_1850
Counts
4 → 339
Calls

4 calls:

68.0ms
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (*.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 (+.f64 alpha beta) (sqrt.f64 (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)))))
16.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
13.0ms
(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))

series1.6s (9.2%)

Counts
4 → 12
Calls

4 calls:

706.0ms
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) (*.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 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))) 1)
358.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
321.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
263.0ms
(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))

simplify175.0ms (1%)

Algorithm
egg-herbie
Counts
351 → 351
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0509017518

prune1.8s (9.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3483351
Fresh178
Picked011
Done101
Total35011361

Merged error: 7.0b

Counts
361 → 11
Compiler

Compiled 25991 to 15708 computations (39.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.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 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1))
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)))))
0.3b
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.5b
(+.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 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))

rewrite659.0ms (3.7%)

Algorithm
rewrite-expression-head
Rules
825×times-frac_binary64_1768
610×*-un-lft-identity_binary64_1762
564×add-sqr-sqrt_binary64_1783
327×add-cube-cbrt_binary64_1794
264×sqrt-prod_binary64_1777
153×associate-*l*_binary64_1705
106×associate-*r*_binary64_1704
89×distribute-lft-out_binary64_1715
68×add-exp-log_binary64_1797
47×add-cbrt-cube_binary64_1795
45×distribute-lft-out--_binary64_1716 difference-of-squares_binary64_1731
42×associate-/r/_binary64_1710
37×div-exp_binary64_1810
35×unswap-sqr_binary64_1730
25×associate-/l*_binary64_1709
23×flip3-+_binary64_1765 flip-+_binary64_1736
22×div-inv_binary64_1759 cbrt-undiv_binary64_1793
15×prod-exp_binary64_1808
14×associate-/r*_binary64_1708
12×sqrt-div_binary64_1778
cbrt-unprod_binary64_1792
add-log-exp_binary64_1798 1-exp_binary64_1803 pow1_binary64_1820
associate-/l/_binary64_1711
frac-2neg_binary64_1773 div-sub_binary64_1767 clear-num_binary64_1761
frac-times_binary64_1772 pow-prod-down_binary64_1830 associate-*l/_binary64_1707 +-commutative_binary64_1694 associate-*r/_binary64_1706 *-commutative_binary64_1695 sum-log_binary64_1850
Counts
4 → 589
Calls

4 calls:

264.0ms
(*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1))
210.0ms
(/.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)))))
6.0ms
(+.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 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))

series1.7s (9.4%)

Counts
4 → 12
Calls

4 calls:

557.0ms
(*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1))
491.0ms
(+.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 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))
365.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
279.0ms
(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify281.0ms (1.6%)

Algorithm
egg-herbie
Counts
601 → 601
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0500235244

prune3.0s (16.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New5965601
Fresh459
Picked011
Done101
Total60111612

Merged error: 7.0b

Counts
612 → 11
Compiler

Compiled 39017 to 23125 computations (40.7% saved)

regimes177.0ms (1%)

Compiler

Compiled 2632 to 1800 computations (31.6% saved)

bsearch43.0ms (0.2%)

Steps
ItersRangePoint
9
1.3426077237192295e+101
4.2466070356158536e+110
3.609134889052862e+103
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06898
16898

end0.0ms (0%)

sample1.5s (8.6%)

Algorithm
intervals
Results
378.0ms6479×body128valid
185.0ms8000×pre128true
158.0ms657×body1024valid
84.0ms498×body512valid
38.0ms308×body256valid
17.0ms58×body2048valid
Compiler

Compiled 759 to 520 computations (31.5% saved)

Profiling

Loading profile data...