Details

Time bar (total: 16.0s)

analyze124.0ms (0.8%)

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 (0.2%)

Algorithm
intervals
Results
11.0ms201×body128valid
6.0ms256×pre128true
3.0ms21×body512valid
3.0ms14×body1024valid
2.0ms19×body256valid
0.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify269.0ms (1.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
0489443
1489443

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 22.6b

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))
2.7b
(+.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)
16.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite98.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64_1805
47×*-un-lft-identity_binary64_1799
25×add-sqr-sqrt_binary64_1821 add-cube-cbrt_binary64_1834
17×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
14×associate-/r/_binary64_1745
11×distribute-lft-out_binary64_1750 flip3-+_binary64_1802 flip-+_binary64_1773
10×associate-/l*_binary64_1744
associate-/l/_binary64_1746
div-exp_binary64_1850 associate-/r*_binary64_1743 cbrt-undiv_binary64_1833 div-inv_binary64_1796
add-log-exp_binary64_1838
frac-times_binary64_1809
pow1_binary64_1860 flip--_binary64_1774 flip3--_binary64_1803
clear-num_binary64_1798 prod-exp_binary64_1848 frac-2neg_binary64_1810 associate-*r/_binary64_1741 cbrt-unprod_binary64_1832 associate-*l/_binary64_1742
sum-log_binary64_1890 +-commutative_binary64_1729
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)
27.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
17.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (9%)

Counts
3 → 9
Calls

3 calls:

695.0ms
(+.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)
609.0ms
(/.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))
125.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify99.0ms (0.6%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049355261
149355261

prune984.0ms (6.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11010120
Fresh000
Picked101
Done000
Total11110121

Merged error: 5.2b

Counts
121 → 10
Compiler

Compiled 24773 to 15252 computations (38.4% saved)

localize13.0ms (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 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.2b
(*.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)))))
4.4b
(+.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)

rewrite184.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
321×times-frac_binary64_1805
290×*-un-lft-identity_binary64_1799
211×add-sqr-sqrt_binary64_1821
140×add-cube-cbrt_binary64_1834
90×associate-*r*_binary64_1739
44×distribute-lft-out_binary64_1750
31×difference-of-squares_binary64_1768 distribute-lft-out--_binary64_1751
26×associate-/l*_binary64_1744
24×associate-/r/_binary64_1745
20×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
15×flip3-+_binary64_1802 flip-+_binary64_1773
12×div-inv_binary64_1796
div-exp_binary64_1850 associate-/r*_binary64_1743 cbrt-undiv_binary64_1833
pow1_binary64_1860 add-log-exp_binary64_1838
associate-*l*_binary64_1740
div-sub_binary64_1804 prod-exp_binary64_1848 unswap-sqr_binary64_1767 associate-/l/_binary64_1746 cbrt-unprod_binary64_1832
clear-num_binary64_1798 frac-2neg_binary64_1810 frac-times_binary64_1809 associate-*l/_binary64_1742
sum-log_binary64_1890 +-commutative_binary64_1729 associate-*r/_binary64_1741 flip--_binary64_1774 flip3--_binary64_1803 *-commutative_binary64_1730 pow-prod-down_binary64_1870
Counts
4 → 295
Calls

4 calls:

54.0ms
(*.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)
23.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
12.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (10.8%)

Counts
4 → 12
Calls

4 calls:

684.0ms
(+.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)
598.0ms
(*.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)))))
328.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
120.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify155.0ms (1%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0496913438
1496913438

prune984.0ms (6.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3025307
Fresh639
Picked011
Done000
Total3089317

Merged error: 5.2b

Counts
317 → 9
Compiler

Compiled 20688 to 11634 computations (43.8% saved)

localize16.0ms (0.1%)

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))))
0.1b
(cbrt.f64 (pow.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) 3))
1.2b
(*.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)))))
4.4b
(+.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)

rewrite196.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
306×times-frac_binary64_1805
275×*-un-lft-identity_binary64_1799
196×add-sqr-sqrt_binary64_1821
133×add-cube-cbrt_binary64_1834
90×associate-*r*_binary64_1739
44×distribute-lft-out_binary64_1750
27×difference-of-squares_binary64_1768 distribute-lft-out--_binary64_1751
22×associate-/r/_binary64_1745
21×associate-/l*_binary64_1744
18×add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
15×flip3-+_binary64_1802 flip-+_binary64_1773
12×cbrt-prod_binary64_1830
11×div-inv_binary64_1796
pow1_binary64_1860 div-exp_binary64_1850 add-log-exp_binary64_1838 cbrt-undiv_binary64_1833
associate-/r*_binary64_1743 associate-*l*_binary64_1740
prod-exp_binary64_1848 unswap-sqr_binary64_1767 unpow-prod-down_binary64_1878 cbrt-unprod_binary64_1832 cube-prod_binary64_1827
div-sub_binary64_1804 cube-div_binary64_1828 cbrt-div_binary64_1831 frac-times_binary64_1809 associate-*l/_binary64_1742
sum-log_binary64_1890 clear-num_binary64_1798 +-commutative_binary64_1729 rem-cbrt-cube_binary64_1823 cube-mult_binary64_1829 pow1/3_binary64_1881 frac-2neg_binary64_1810 associate-*r/_binary64_1741 associate-/l/_binary64_1746 unpow3_binary64_1865 sqr-pow_binary64_1771 *-commutative_binary64_1730 pow-prod-down_binary64_1870
Counts
4 → 278
Calls

4 calls:

48.0ms
(*.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)))))
38.0ms
(cbrt.f64 (pow.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) 3))
34.0ms
(+.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)
22.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series2.3s (14.1%)

Counts
4 → 12
Calls

4 calls:

686.0ms
(+.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)
679.0ms
(cbrt.f64 (pow.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) 3))
582.0ms
(*.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)))))
309.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify149.0ms (0.9%)

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0507713897

prune1.1s (7.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2846290
Fresh437
Picked101
Done011
Total28910299

Merged error: 5.2b

Counts
299 → 10
Compiler

Compiled 23049 to 13510 computations (41.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.6b
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
1.6b
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
5.6b
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite302.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
378×times-frac_binary64_1805
278×*-un-lft-identity_binary64_1799
233×cbrt-prod_binary64_1830
216×associate-*r*_binary64_1739
214×add-sqr-sqrt_binary64_1821
172×add-cube-cbrt_binary64_1834
97×add-exp-log_binary64_1837
55×add-cbrt-cube_binary64_1835
45×prod-exp_binary64_1848 cbrt-unprod_binary64_1832
32×distribute-lft-out_binary64_1750
30×div-exp_binary64_1850 cbrt-undiv_binary64_1833
21×difference-of-squares_binary64_1768 distribute-lft-out--_binary64_1751
16×associate-/r/_binary64_1745
15×flip3-+_binary64_1802 flip-+_binary64_1773
pow1_binary64_1860 frac-times_binary64_1809 associate-*l/_binary64_1742
div-inv_binary64_1796
add-log-exp_binary64_1838 cbrt-div_binary64_1831
associate-*r/_binary64_1741 pow-prod-down_binary64_1870
pow1/3_binary64_1881
sum-log_binary64_1890 +-commutative_binary64_1729 associate-*l*_binary64_1740 *-commutative_binary64_1730
Counts
4 → 313
Calls

4 calls:

106.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
77.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
7.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
7.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series2.0s (12.4%)

Counts
4 → 12
Calls

4 calls:

738.0ms
(+.f64 (*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)
646.0ms
(*.f64 (*.f64 (+.f64 alpha beta) (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))) (/.f64 (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
299.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
294.0ms
(cbrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify246.0ms (1.5%)

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
0497825817
1497825817

prune1.8s (11.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3232325
Fresh448
Picked011
Done011
Total3278335

Merged error: 5.2b

Counts
335 → 8
Compiler

Compiled 32964 to 17888 computations (45.7% saved)

regimes148.0ms (0.9%)

Compiler

Compiled 2008 to 1280 computations (36.3% saved)

bsearch117.0ms (0.7%)

Steps
ItersRangePoint
9
1.2495524567113899e+190
6.878330910785561e+198
1.0163560453529555e+192
7
1.6297253199976274e+135
4.874760934320271e+136
3.765248146023335e+135
6
3.0534126405769425e+97
4.550104348700514e+98
4.449160688824685e+97
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094230
194230

end0.0ms (0%)

sample1.5s (9.1%)

Algorithm
intervals
Results
371.0ms6482×body128valid
188.0ms8000×pre128true
155.0ms676×body1024valid
84.0ms488×body512valid
36.0ms303×body256valid
15.0ms51×body2048valid
Compiler

Compiled 688 to 439 computations (36.2% saved)

Profiling

Loading profile data...