Details

analyze13.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify240.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5184	22

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 21.6b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
21.4b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1746`
7×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
5×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `add-log-exp_binary64_1838` `*-un-lft-identity_binary64_1799` `frac-times_binary64_1809`
3×	`associate-/r*_binary64_1743` `flip--_binary64_1774` `flip3--_binary64_1803` `times-frac_binary64_1805`
2×	`pow1_binary64_1860` `div-exp_binary64_1850` `associate-r/_binary64_1741` `associate-/r/_binary64_1745` `cbrt-undiv_binary64_1833` `associate-l/_binary64_1742`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `associate-/l*_binary64_1744` `prod-exp_binary64_1848` `frac-2neg_binary64_1810` `cbrt-unprod_binary64_1832` `div-inv_binary64_1796`

Counts

2 → 42

Calls

2 calls:

14.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series131.0ms (4.3%)

Counts

2 → 6

Calls

2 calls:

93.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
38.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify35.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5033	969

prune113.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Merged error: 0.2b

Counts

49 → 7

Compiler

Compiled 2750 to 896 computations (67.4% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite94.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64_1821`
96×	`times-frac_binary64_1805`
95×	`*-un-lft-identity_binary64_1799`
57×	`add-cube-cbrt_binary64_1834` `sqrt-prod_binary64_1815`
36×	`associate-l_binary64_1740`
30×	`associate-r_binary64_1739`
18×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
13×	`difference-of-squares_binary64_1768` `distribute-lft-out--_binary64_1751`
10×	`sqrt-div_binary64_1816`
9×	`unswap-sqr_binary64_1767`
8×	`pow1_binary64_1860`
6×	`associate-/r*_binary64_1743` `associate-/r/_binary64_1745` `distribute-lft-out_binary64_1750`
5×	`div-exp_binary64_1850` `associate-/l*_binary64_1744` `cbrt-undiv_binary64_1833` `flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`add-log-exp_binary64_1838` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
3×	`div-inv_binary64_1796`
2×	`pow1/2_binary64_1879` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`
1×	`div-sub_binary64_1804` `clear-num_binary64_1798` `frac-2neg_binary64_1810` `associate-r/_binary64_1741` `flip--_binary64_1774` `flip3--_binary64_1803` `-commutative_binary64_1730` `pow-prod-down_binary64_1870` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 183

Calls

4 calls:

44.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
14.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series306.0ms (10%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
96.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
49.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
43.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify93.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4964	5945
1	4964	5945

prune179.0ms (5.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	195	7	202

Merged error: 0.2b

Counts

202 → 7

Compiler

Compiled 6955 to 742 computations (89.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (*.f64 y y)))))
21.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
21.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
21.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite106.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64_1821`
90×	`times-frac_binary64_1805`
84×	`cbrt-prod_binary64_1830`
67×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
24×	`difference-of-squares_binary64_1768`
21×	`associate-l_binary64_1740` `swap-sqr_binary64_1766` `associate-r_binary64_1739`
14×	`associate-/r/_binary64_1745`
12×	`associate-/l*_binary64_1744` `add-exp-log_binary64_1837`
11×	`pow1_binary64_1860`
10×	`add-cbrt-cube_binary64_1835`
9×	`unswap-sqr_binary64_1767` `associate-/r*_binary64_1743`
7×	`div-inv_binary64_1796` `flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`pow1/3_binary64_1881` `associate-/l/_binary64_1746`
4×	`add-log-exp_binary64_1838` `cbrt-div_binary64_1831`
3×	`div-sub_binary64_1804` `clear-num_binary64_1798` `div-exp_binary64_1850` `frac-2neg_binary64_1810` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-undiv_binary64_1833`
2×	`pow-sqr_binary64_1772` `pow-prod-up_binary64_1869` `pow-prod-down_binary64_1870`
1×	`pow2_binary64_1880` `prod-exp_binary64_1848` `associate-r/_binary64_1741` `cbrt-unprod_binary64_1832` `-commutative_binary64_1730` `pow-plus_binary64_1862` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 201

Calls

4 calls:

36.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (*.f64 y y)))))
11.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
11.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
10.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

series411.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (*.f64 y y)))))
67.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
66.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
64.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

simplify103.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5040	8625

prune255.0ms (8.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	213	7	220

Merged error: 0.2b

Counts

220 → 7

Compiler

Compiled 13014 to 968 computations (92.6% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	3	3
Total	7	7

Merged error: 0.2b

Counts

7 → 7

Compiler

Compiled 0 to 0 computations (0% saved)

regimes78.0ms (2.6%)

Compiler: Compiled 472 to 236 computations (50% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	50
1	27	50

end0.0ms (0%)

sample803.0ms (26.3%)

Algorithm

1×

intervals

Results

298.0ms	8000×	body	128	valid
171.0ms	8000×	pre	128	true

Compiler

Compiled 239 to 122 computations (49% saved)

Details

analyze13.0ms (0.4%)

sample22.0ms (0.7%)

simplify240.0ms (7.9%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite23.0ms (0.7%)

series131.0ms (4.3%)

simplify35.0ms (1.1%)

prune113.0ms (3.7%)

localize11.0ms (0.4%)

rewrite94.0ms (3.1%)

series306.0ms (10%)

simplify93.0ms (3.1%)

prune179.0ms (5.9%)

localize11.0ms (0.4%)

rewrite106.0ms (3.5%)

series411.0ms (13.5%)

simplify103.0ms (3.4%)

prune255.0ms (8.3%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.3%)

prune1.0ms (0%)

regimes78.0ms (2.6%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample803.0ms (26.3%)

Profiling