Details

Time bar (total: 2.6s)

analyze4.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample18.0ms (0.7%)

Algorithm
intervals
Results
5.0ms58×body512valid
4.0ms147×body128valid
2.0ms40×body256valid
1.0ms11×body1024valid
Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify175.0ms (6.8%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
07616
17616

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 13.2b

Counts
2 → 1
Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 1 (+.f64 x 1))
0.0b
(/.f64 1 (-.f64 x 1))
4.3b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite65.0ms (2.5%)

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity_binary64_1799
95×add-sqr-sqrt_binary64_1821
90×times-frac_binary64_1805
43×add-cube-cbrt_binary64_1834
30×distribute-lft-out--_binary64_1751
27×cancel-sign-sub-inv_binary64_1765
23×difference-of-squares_binary64_1768
11×associate-/r*_binary64_1743 add-exp-log_binary64_1837
10×distribute-lft-out_binary64_1750
associate-/r/_binary64_1745
add-cbrt-cube_binary64_1835 difference-of-sqr-1_binary64_1769 div-inv_binary64_1796
associate-/l*_binary64_1744
pow1_binary64_1860 add-log-exp_binary64_1838
div-exp_binary64_1850 flip--_binary64_1774
flip3--_binary64_1803
clear-num_binary64_1798 rec-exp_binary64_1849 frac-2neg_binary64_1810 pow-flip_binary64_1873 1-exp_binary64_1843 cbrt-undiv_binary64_1833 inv-pow_binary64_1884 flip-+_binary64_1773
sub-neg_binary64_1792 diff-log_binary64_1891 frac-sub_binary64_1808 flip3-+_binary64_1802
Counts
3 → 151
Calls

3 calls:

37.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
7.0ms
(/.f64 1 (-.f64 x 1))
6.0ms
(/.f64 1 (+.f64 x 1))

series112.0ms (4.4%)

Counts
3 → 9
Calls

3 calls:

75.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
20.0ms
(/.f64 1 (-.f64 x 1))
18.0ms
(/.f64 1 (+.f64 x 1))

simplify80.0ms (3.1%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
054212407

prune175.0ms (6.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1591160
Fresh000
Picked101
Done000
Total1601161

Merged error: 0.3b

Counts
161 → 1
Compiler

Compiled 2837 to 2328 computations (17.9% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.3b
(/.f64 -2 (+.f64 -1 (*.f64 x x)))

rewrite7.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1821 add-cube-cbrt_binary64_1834 *-un-lft-identity_binary64_1799 times-frac_binary64_1805
associate-/l*_binary64_1744 associate-/r*_binary64_1743 add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
associate-/r/_binary64_1745
pow1_binary64_1860 clear-num_binary64_1798 div-exp_binary64_1850 add-log-exp_binary64_1838 frac-2neg_binary64_1810 cbrt-undiv_binary64_1833 div-inv_binary64_1796 flip3-+_binary64_1802 flip-+_binary64_1773
Counts
1 → 29
Calls

1 calls:

5.0ms
(/.f64 -2 (+.f64 -1 (*.f64 x x)))

series45.0ms (1.7%)

Counts
1 → 3
Calls

1 calls:

45.0ms
(/.f64 -2 (+.f64 -1 (*.f64 x x)))

simplify67.0ms (2.6%)

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
05269557

prune61.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New30232
Fresh000
Picked011
Done000
Total30333

Merged error: 0.2b

Counts
33 → 3
Compiler

Compiled 946 to 679 computations (28.2% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.2b
(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
24.3b
(*.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (*.f64 x x)))

rewrite43.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt_binary64_1821
67×*-un-lft-identity_binary64_1799
61×times-frac_binary64_1805
43×difference-of-squares_binary64_1768
36×associate-*l*_binary64_1740
32×add-cube-cbrt_binary64_1834
14×unpow-prod-down_binary64_1878 sqr-pow_binary64_1771
10×associate-/r*_binary64_1743
add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837
distribute-lft-out--_binary64_1751
pow1_binary64_1860 flip--_binary64_1774 associate-/r/_binary64_1745 flip3--_binary64_1803 associate-*r*_binary64_1739
associate-/l*_binary64_1744
distribute-rgt-in_binary64_1749 sub-neg_binary64_1792 div-exp_binary64_1850 distribute-lft-in_binary64_1748 add-log-exp_binary64_1838 prod-exp_binary64_1848 unswap-sqr_binary64_1767 associate-*r/_binary64_1741 cbrt-undiv_binary64_1833 cbrt-unprod_binary64_1832 div-inv_binary64_1796 cancel-sign-sub-inv_binary64_1765 frac-times_binary64_1809
clear-num_binary64_1798 frac-2neg_binary64_1810 *-commutative_binary64_1730 pow-prod-down_binary64_1870 associate-*l/_binary64_1742
Counts
2 → 121
Calls

2 calls:

20.0ms
(*.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (*.f64 x x)))
9.0ms
(/.f64 -2 (-.f64 1 (pow.f64 x 4)))

series180.0ms (7%)

Counts
2 → 6
Calls

2 calls:

114.0ms
(/.f64 -2 (-.f64 1 (pow.f64 x 4)))
66.0ms
(*.f64 (/.f64 -2 (-.f64 1 (pow.f64 x 4))) (-.f64 -1 (*.f64 x x)))

simplify67.0ms (2.6%)

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051612590

prune159.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1270127
Fresh011
Picked011
Done011
Total1273130

Merged error: 0.2b

Counts
130 → 3
Compiler

Compiled 2775 to 2053 computations (26% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 (/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x)))) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
16.8b
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
16.8b
(sqrt.f64 (+.f64 -1 (*.f64 x x)))

rewrite57.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
270×times-frac_binary64_1805
148×add-sqr-sqrt_binary64_1821
146×add-cube-cbrt_binary64_1834 *-un-lft-identity_binary64_1799
144×sqrt-prod_binary64_1815
24×associate-/l*_binary64_1744
20×sqrt-div_binary64_1816
16×associate-/r/_binary64_1745
10×flip3-+_binary64_1802 flip-+_binary64_1773
add-cbrt-cube_binary64_1835 add-exp-log_binary64_1837 div-inv_binary64_1796
associate-/r*_binary64_1743
pow1_binary64_1860
div-exp_binary64_1850 add-log-exp_binary64_1838 cbrt-undiv_binary64_1833
pow1/2_binary64_1879 sqrt-pow1_binary64_1817 rem-sqrt-square_binary64_1812
clear-num_binary64_1798 frac-2neg_binary64_1810 associate-/l/_binary64_1746
Counts
3 → 221
Calls

3 calls:

17.0ms
(/.f64 (/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x)))) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
5.0ms
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms
(sqrt.f64 (+.f64 -1 (*.f64 x x)))

series130.0ms (5%)

Counts
3 → 9
Calls

3 calls:

47.0ms
(/.f64 (/.f64 -2 (sqrt.f64 (+.f64 -1 (*.f64 x x)))) (sqrt.f64 (+.f64 -1 (*.f64 x x))))
45.0ms
(sqrt.f64 (+.f64 -1 (*.f64 x x)))
38.0ms
(sqrt.f64 (+.f64 -1 (*.f64 x x)))

simplify130.0ms (5%)

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
053447669

prune365.0ms (14.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2300230
Fresh000
Picked011
Done022
Total2303233

Merged error: 0.2b

Counts
233 → 3
Compiler

Compiled 5854 to 4013 computations (31.4% saved)

regimes9.0ms (0.4%)

Compiler

Compiled 37 to 30 computations (18.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
1810

end0.0ms (0%)

sample599.0ms (23.2%)

Algorithm
intervals
Results
162.0ms1963×body512valid
141.0ms4579×body128valid
59.0ms1000×body256valid
52.0ms458×body1024valid
Compiler

Compiled 54 to 46 computations (14.8% saved)

Profiling

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