Details

Time bar (total: 3.7s)

analyze127.0ms (3.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%68.7%6.3%6
25%53.1%22%7
25%46.8%28.2%8
25%33.6%41.5%9
28.1%18%54%10
31.6%12.1%56.3%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 30 to 20 computations (33.3% saved)

sample22.0ms (0.6%)

Algorithm
intervals
Results
15.0ms256×body128valid
Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify229.0ms (6.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
0507043

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1
Compiler

Compiled 58 to 38 computations (34.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
0.0b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.9b
(*.f64 (*.f64 b b) (+.f64 3 a))

rewrite49.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64_1805 add-exp-log_binary64_1821 *-un-lft-identity_binary64_1783 pow1_binary64_1844
14×add-cbrt-cube_binary64_1819
10×add-cube-cbrt_binary64_1818 associate-*r*_binary64_1723
distribute-lft-in_binary64_1732 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 cancel-sign-sub-inv_binary64_1749 distribute-rgt-in_binary64_1733 pow-prod-down_binary64_1854 add-log-exp_binary64_1822
associate-*r/_binary64_1725
pow-unpow_binary64_1860 unpow-prod-down_binary64_1862
associate-+r+_binary64_1715 difference-of-squares_binary64_1752 flip-+_binary64_1757 associate-*l*_binary64_1724 *-commutative_binary64_1714 flip3-+_binary64_1786 unswap-sqr_binary64_1751 sub-neg_binary64_1776
flip3--_binary64_1787 +-commutative_binary64_1713 sqr-pow_binary64_1755 distribute-lft-out_binary64_1734 unpow2_binary64_1848 distribute-lft-out--_binary64_1735 sum-log_binary64_1874 pow-pow_binary64_1855 flip--_binary64_1758 pow-to-exp_binary64_1852 pow-exp_binary64_1851
Counts
4 → 87
Calls

4 calls:

13.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
11.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
10.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
6.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

series298.0ms (8.1%)

Counts
4 → 12
Calls

4 calls:

135.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
64.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
50.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
48.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))

simplify54.0ms (1.5%)

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050741789

prune153.0ms (4.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New97299
Fresh000
Picked101
Done000
Total982100

Merged error: 0b

Counts
100 → 2
Compiler

Compiled 3441 to 1754 computations (49% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 b b) (*.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
0.0b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.9b
(*.f64 (*.f64 b b) (+.f64 3 a))
1.7b
(*.f64 (*.f64 b b) (*.f64 a a))

rewrite81.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
42×pow1_binary64_1844
32×associate-*r/_binary64_1725
26×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
20×frac-add_binary64_1791 pow-prod-down_binary64_1854
14×cbrt-unprod_binary64_1816 prod-exp_binary64_1832 flip-+_binary64_1757 flip3-+_binary64_1786
13×add-sqr-sqrt_binary64_1805 *-un-lft-identity_binary64_1783 add-log-exp_binary64_1822
11×associate-*r*_binary64_1723
add-cube-cbrt_binary64_1818
distribute-lft-in_binary64_1732 cancel-sign-sub-inv_binary64_1749 distribute-rgt-in_binary64_1733 sum-log_binary64_1874
flip3--_binary64_1787 flip--_binary64_1758
pow-plus_binary64_1846 pow-prod-up_binary64_1853
associate-*l*_binary64_1724 *-commutative_binary64_1714 unswap-sqr_binary64_1751
associate-+r+_binary64_1715 difference-of-squares_binary64_1752 pow-sqr_binary64_1756 sub-neg_binary64_1776 pow2_binary64_1864
+-commutative_binary64_1713 distribute-lft-out_binary64_1734 distribute-lft-out--_binary64_1735 associate-+l+_binary64_1716
Counts
4 → 113
Calls

4 calls:

29.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 b b) (*.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
11.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
11.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
10.0ms
(*.f64 (*.f64 b b) (*.f64 a a))

series302.0ms (8.2%)

Counts
4 → 12
Calls

4 calls:

141.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 b b) (*.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
67.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
51.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
43.0ms
(*.f64 (*.f64 b b) (*.f64 a a))

simplify99.0ms (2.7%)

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049424559
149424559

prune286.0ms (7.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1250125
Fresh011
Picked011
Done000
Total1252127

Merged error: 0b

Counts
127 → 2
Compiler

Compiled 6385 to 3733 computations (41.5% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 a (-.f64 a (*.f64 a a))) (*.f64 (*.f64 b b) (+.f64 3 a)))))
0.0b
(*.f64 a (-.f64 a (*.f64 a a)))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.9b
(*.f64 (*.f64 b b) (+.f64 3 a))

rewrite44.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_1805
12×add-exp-log_binary64_1821 *-un-lft-identity_binary64_1783 pow1_binary64_1844
11×add-cbrt-cube_binary64_1819
add-cube-cbrt_binary64_1818 associate-*r*_binary64_1723
add-log-exp_binary64_1822
associate-*r/_binary64_1725 distribute-lft-in_binary64_1732 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l*_binary64_1724 distribute-rgt-in_binary64_1733 pow-prod-down_binary64_1854
pow-unpow_binary64_1860 unpow-prod-down_binary64_1862
associate-+r+_binary64_1715 flip-+_binary64_1757 cancel-sign-sub-inv_binary64_1749 *-commutative_binary64_1714 flip3-+_binary64_1786 unswap-sqr_binary64_1751 sub-neg_binary64_1776
flip3--_binary64_1787 difference-of-squares_binary64_1752 +-commutative_binary64_1713 sqr-pow_binary64_1755 distribute-lft-out_binary64_1734 unpow2_binary64_1848 sum-log_binary64_1874 pow-pow_binary64_1855 flip--_binary64_1758 distribute-rgt-out--_binary64_1737 pow-to-exp_binary64_1852 pow-exp_binary64_1851
Counts
4 → 81
Calls

4 calls:

10.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 a (-.f64 a (*.f64 a a))) (*.f64 (*.f64 b b) (+.f64 3 a)))))
10.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
9.0ms
(*.f64 a (-.f64 a (*.f64 a a)))
5.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

series308.0ms (8.3%)

Counts
4 → 12
Calls

4 calls:

137.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 a (-.f64 a (*.f64 a a))) (*.f64 (*.f64 b b) (+.f64 3 a)))))
77.0ms
(*.f64 a (-.f64 a (*.f64 a a)))
49.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
45.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))

simplify40.0ms (1.1%)

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
051881745

prune115.0ms (3.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New93093
Fresh000
Picked011
Done011
Total93295

Merged error: 0b

Counts
95 → 2
Compiler

Compiled 3219 to 1430 computations (55.6% saved)

regimes259.0ms (7%)

Compiler

Compiled 4100 to 2621 computations (36.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05452
15452

end0.0ms (0%)

sample1.2s (31.8%)

Algorithm
intervals
Results
507.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 747 to 485 computations (35.1% saved)

Profiling

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