Details

Time bar (total: 3.5s)

analyze13.0ms (0.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
0%50%50%2
0%50%50%3
37.5%12.5%50%4
43.7%6.2%50%5
46.9%3.1%50%6
48.4%1.6%50%7
49.2%0.8%50%8
49.6%0.4%50%9
49.8%0.2%50%10
49.9%0.1%50%11
49.9%0%50%12
50%0%50%13
50%0%50%14
Compiler

Compiled 29 to 20 computations (31% saved)

sample23.0ms (0.7%)

Algorithm
1×intervals
Results
13.0ms256×body128valid
3.0ms256×pre128true
Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify136.0ms (3.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0504713

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 2
Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.6b
(/.f64 1 (*.f64 i i))

rewrite22.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64_1805
35×times-frac_binary64_1789
33×*-un-lft-identity_binary64_1783
17×add-cube-cbrt_binary64_1818
15×add-exp-log_binary64_1821
12×difference-of-squares_binary64_1752
10×pow1_binary64_1844
9×add-cbrt-cube_binary64_1819 associate-/r*_binary64_1727
8×distribute-lft-out--_binary64_1735
6×associate-/l*_binary64_1728 div-inv_binary64_1780 pow-flip_binary64_1857
5×div-exp_binary64_1834
3×prod-exp_binary64_1832 cbrt-undiv_binary64_1817
2×associate-/r/_binary64_1729 1-exp_binary64_1827 frac-2neg_binary64_1794 clear-num_binary64_1782 rec-exp_binary64_1833 add-log-exp_binary64_1822
1×flip3--_binary64_1787 inv-pow_binary64_1868 cbrt-unprod_binary64_1816 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow-sqr_binary64_1756 pow-prod-down_binary64_1854 flip--_binary64_1758 pow2_binary64_1864
Counts
2 → 81
Calls

2 calls:

11.0ms
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms
(/.f64 1 (*.f64 i i))

series21.0ms (0.6%)

Counts
2 → 6
Calls

2 calls:

12.0ms
(/.f64 1 (*.f64 i i))
9.0ms
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

simplify92.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
047991185
147991185

prune87.0ms (2.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New85287
Fresh011
Picked101
Done000
Total86389

Merged error: 0b

Counts
89 → 3
Compiler

Compiled 1232 to 939 computations (23.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
0.1b
(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
0.6b
(/.f64 1 (*.f64 i i))
28.1b
(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite100.0ms (2.9%)

Algorithm
1×rewrite-expression-head
Rules
528×times-frac_binary64_1789
424×add-sqr-sqrt_binary64_1805
388×*-un-lft-identity_binary64_1783
273×sqrt-prod_binary64_1799
156×add-cube-cbrt_binary64_1818
152×difference-of-squares_binary64_1752
57×distribute-lft-out--_binary64_1735
49×distribute-lft-out_binary64_1734
38×div-inv_binary64_1780
34×associate-/r/_binary64_1729
24×associate-/l*_binary64_1728
22×add-exp-log_binary64_1821
21×pow1_binary64_1844
19×associate-/r*_binary64_1727
16×add-cbrt-cube_binary64_1819 flip-+_binary64_1757 flip3-+_binary64_1786
12×pow-flip_binary64_1857
8×div-exp_binary64_1834 sqrt-pow1_binary64_1801
6×cbrt-undiv_binary64_1817
4×add-log-exp_binary64_1822
3×prod-exp_binary64_1832 frac-2neg_binary64_1794 clear-num_binary64_1782 rem-sqrt-square_binary64_1796
2×inv-pow_binary64_1868 1-exp_binary64_1827 pow-plus_binary64_1846 pow-prod-up_binary64_1853 pow-sqr_binary64_1756 pow-prod-down_binary64_1854 rec-exp_binary64_1833 pow2_binary64_1864
1×flip3--_binary64_1787 associate-/l/_binary64_1730 cbrt-unprod_binary64_1816 pow1/2_binary64_1863 sqrt-div_binary64_1800 flip--_binary64_1758
Counts
4 → 393
Calls

4 calls:

21.0ms
(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
5.0ms
(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
5.0ms
(/.f64 1 (*.f64 i i))
5.0ms
(sqrt.f64 (/.f64 1 (*.f64 i i)))

series77.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

33.0ms
(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
27.0ms
(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
11.0ms
(/.f64 1 (*.f64 i i))
6.0ms
(sqrt.f64 (/.f64 1 (*.f64 i i)))

simplify191.0ms (5.5%)

Algorithm
1×egg-herbie
Counts
405 → 405
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0512414912

prune946.0ms (27.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New4050405
Fresh022
Picked011
Done000
Total4053408

Merged error: 0b

Counts
408 → 3
Compiler

Compiled 11619 to 10126 computations (12.8% saved)

localize6.0ms (0.2%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done011
Total033

Merged error: 0b

Counts
3 → 3
Compiler

Compiled 25 to 17 computations (32% saved)

localize16.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.1b
(*.f64 (*.f64 i i) (*.f64 i i))
13.1b
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
43.8b
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

rewrite111.0ms (3.2%)

Algorithm
1×rewrite-expression-head
Rules
302×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
168×cbrt-unprod_binary64_1816 prod-exp_binary64_1832
114×pow1_binary64_1844
76×cbrt-undiv_binary64_1817 div-exp_binary64_1834
38×times-frac_binary64_1789
36×pow-prod-up_binary64_1853
23×pow-prod-down_binary64_1854
22×add-sqr-sqrt_binary64_1805 *-un-lft-identity_binary64_1783 pow-sqr_binary64_1756
18×pow-plus_binary64_1846
16×add-cube-cbrt_binary64_1818
13×pow2_binary64_1864
12×difference-of-squares_binary64_1752
9×div-inv_binary64_1780
7×associate-/r*_binary64_1727
6×associate-/l*_binary64_1728 difference-of-sqr-1_binary64_1753
3×add-log-exp_binary64_1822
2×associate-/r/_binary64_1729 frac-2neg_binary64_1794 clear-num_binary64_1782
1×flip3--_binary64_1787 associate-/l/_binary64_1730 swap-sqr_binary64_1750 associate-*l*_binary64_1724 *-commutative_binary64_1714 unswap-sqr_binary64_1751 flip--_binary64_1758 associate-*r*_binary64_1723
Counts
3 → 232
Calls

3 calls:

37.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
25.0ms
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))
9.0ms
(*.f64 (*.f64 i i) (*.f64 i i))

series57.0ms (1.7%)

Counts
3 → 9
Calls

3 calls:

20.0ms
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))
20.0ms
(*.f64 (*.f64 i i) (*.f64 i i))
17.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

simplify254.0ms (7.3%)

Algorithm
1×egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049003427
149003427

prune268.0ms (7.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2410241
Fresh000
Picked011
Done022
Total2413244

Merged error: 0b

Counts
244 → 3
Compiler

Compiled 4778 to 3537 computations (26% saved)

regimes65.0ms (1.9%)

Compiler

Compiled 618 to 528 computations (14.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03422
13422

end0.0ms (0%)

sample953.0ms (27.4%)

Algorithm
1×intervals
Results
403.0ms8000×body128valid
94.0ms8000×pre128true
Compiler

Compiled 327 to 281 computations (14.1% saved)

Profiling

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