Details

Time bar (total: 11.9s)

analyze42.0ms (0.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14
Compiler

Compiled 63 to 34 computations (46% saved)

sample41.0ms (0.3%)

Algorithm
1×intervals
Results
25.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify129.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0539579

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 52.5b

Counts
2 → 1
Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
34.1b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
45.0b
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite148.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
86×times-frac_binary64_1789
66×associate-/r/_binary64_1729 flip-+_binary64_1757 flip3-+_binary64_1786
61×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
46×add-sqr-sqrt_binary64_1805
44×*-un-lft-identity_binary64_1783 frac-times_binary64_1793
34×associate-*r/_binary64_1725
30×add-cube-cbrt_binary64_1818
28×difference-of-squares_binary64_1752
22×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l/_binary64_1726
19×cbrt-undiv_binary64_1817 div-exp_binary64_1834
16×pow1_binary64_1844
14×associate-/l*_binary64_1728 difference-of-sqr-1_binary64_1753
9×associate-/l/_binary64_1730 div-inv_binary64_1780
7×associate-/r*_binary64_1727
6×associate-*r*_binary64_1723
4×associate-*l*_binary64_1724 pow-prod-down_binary64_1854 add-log-exp_binary64_1822
3×swap-sqr_binary64_1750
2×distribute-lft-in_binary64_1732 *-commutative_binary64_1714 frac-2neg_binary64_1794 distribute-rgt-in_binary64_1733 clear-num_binary64_1782
1×flip3--_binary64_1787 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow-sqr_binary64_1756 unswap-sqr_binary64_1751 flip--_binary64_1758 pow2_binary64_1864
Counts
4 → 228
Calls

4 calls:

41.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
29.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
13.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))

series1.9s (16%)

Counts
4 → 12
Calls

4 calls:

1.5s
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
209.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
95.0ms
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))
47.0ms
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify158.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0526118181

prune640.0ms (5.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2328240
Fresh000
Picked101
Done000
Total2338241

Merged error: 31.9b

Counts
241 → 8
Compiler

Compiled 17735 to 6672 computations (62.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.5b
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
30.7b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite120.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
240×times-frac_binary64_1789
174×*-un-lft-identity_binary64_1783
170×add-sqr-sqrt_binary64_1805
106×add-cube-cbrt_binary64_1818
34×associate-/r/_binary64_1729
32×difference-of-squares_binary64_1752
28×associate-/l*_binary64_1728
25×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
18×flip-+_binary64_1757 flip3-+_binary64_1786
17×div-inv_binary64_1780 associate-/r*_binary64_1727
16×difference-of-sqr-1_binary64_1753 distribute-lft-out--_binary64_1735
11×cbrt-undiv_binary64_1817 div-exp_binary64_1834
10×distribute-lft-out_binary64_1734
6×associate-/l/_binary64_1730
4×frac-2neg_binary64_1794 clear-num_binary64_1782 add-log-exp_binary64_1822 pow1_binary64_1844
2×associate-*r/_binary64_1725 cbrt-unprod_binary64_1816 prod-exp_binary64_1832
1×flip3--_binary64_1787 flip--_binary64_1758
Counts
4 → 268
Calls

4 calls:

21.0ms
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
21.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
13.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series476.0ms (4%)

Counts
4 → 12
Calls

4 calls:

194.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
111.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
108.0ms
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
62.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify182.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0495216880
1495216880

prune917.0ms (7.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2746280
Fresh437
Picked011
Done000
Total27810288

Merged error: 31.9b

Counts
288 → 10
Compiler

Compiled 21410 to 8740 computations (59.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(/.f64 (/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.5b
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
21.3b
(/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
32.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite157.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
270×times-frac_binary64_1789
190×*-un-lft-identity_binary64_1783
180×add-sqr-sqrt_binary64_1805
116×add-cube-cbrt_binary64_1818
34×add-cbrt-cube_binary64_1819 associate-/r/_binary64_1729 add-exp-log_binary64_1821
32×difference-of-squares_binary64_1752
31×associate-/l*_binary64_1728
21×sqrt-prod_binary64_1799
20×associate-/r*_binary64_1727
19×flip-+_binary64_1757 flip3-+_binary64_1786
17×div-inv_binary64_1780
16×difference-of-sqr-1_binary64_1753 distribute-lft-out--_binary64_1735 cbrt-undiv_binary64_1817 div-exp_binary64_1834
13×distribute-lft-out_binary64_1734
12×sqrt-div_binary64_1800
9×associate-/l/_binary64_1730
4×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 frac-2neg_binary64_1794 clear-num_binary64_1782 add-log-exp_binary64_1822 pow1_binary64_1844
2×associate-*r/_binary64_1725 frac-times_binary64_1793
1×flip3--_binary64_1787 associate-*l/_binary64_1726 flip--_binary64_1758
Counts
4 → 296
Calls

4 calls:

31.0ms
(/.f64 (/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
24.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
23.0ms
(/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
11.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series600.0ms (5.1%)

Counts
4 → 12
Calls

4 calls:

199.0ms
(/.f64 (/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
188.0ms
(/.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
108.0ms
(/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
103.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify203.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
308 → 308
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0499019083
1499019083

prune1.1s (9.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3053308
Fresh268
Picked101
Done011
Total30810318

Merged error: 23.7b

Counts
318 → 10
Compiler

Compiled 25911 to 11347 computations (56.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(*.f64 (sqrt.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))))
21.3b
(/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
32.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
32.1b
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite131.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
90×add-sqr-sqrt_binary64_1805
80×sqrt-prod_binary64_1799
68×times-frac_binary64_1789
56×add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
20×swap-sqr_binary64_1750
19×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 pow1_binary64_1844
18×associate-*l*_binary64_1724 associate-*r*_binary64_1723
14×associate-/r/_binary64_1729
12×associate-/r*_binary64_1727
11×flip-+_binary64_1757 flip3-+_binary64_1786
9×associate-/l/_binary64_1730 unswap-sqr_binary64_1751
8×pow1/2_binary64_1863 sqrt-pow1_binary64_1801
7×associate-/l*_binary64_1728 div-inv_binary64_1780
6×sqrt-div_binary64_1800 cbrt-undiv_binary64_1817 div-exp_binary64_1834
5×pow-prod-up_binary64_1853
4×rem-sqrt-square_binary64_1796 add-log-exp_binary64_1822
3×associate-*r/_binary64_1725 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 pow-sqr_binary64_1756 frac-2neg_binary64_1794 frac-times_binary64_1793 clear-num_binary64_1782 pow-prod-down_binary64_1854
2×associate-*l/_binary64_1726 sqr-abs_binary64_1798
1×sqrt-unprod_binary64_1803 pow-plus_binary64_1846 *-commutative_binary64_1714 rem-square-sqrt_binary64_1795 pow2_binary64_1864
Counts
4 → 193
Calls

4 calls:

31.0ms
(*.f64 (sqrt.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))))
23.0ms
(/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
13.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
11.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series522.0ms (4.4%)

Counts
4 → 12
Calls

4 calls:

200.0ms
(*.f64 (sqrt.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (sqrt.f64 (/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))))
111.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
107.0ms
(/.f64 (+.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
103.0ms
(/.f64 (*.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)))) (+.f64 i (+.f64 alpha beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

simplify108.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
053718361

prune746.0ms (6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2041205
Fresh178
Picked011
Done011
Total20510215

Merged error: 23.7b

Counts
215 → 10
Compiler

Compiled 19078 to 7725 computations (59.5% saved)

regimes806.0ms (6.8%)

Compiler

Compiled 14108 to 7221 computations (48.8% saved)

bsearch9.0ms (0.1%)

Compiler

Compiled 53 to 27 computations (49.1% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
062237
162237

end0.0ms (0%)

sample2.6s (22.2%)

Algorithm
1×intervals
Results
669.0ms8000×body128valid
188.0ms8000×pre128true
Compiler

Compiled 3680 to 1879 computations (48.9% saved)

Profiling

Loading profile data...