Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample33.0ms (0.3%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify425.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (259.0ms)

Iter	Nodes	Cost
0	5111	37

prune10.0ms (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: 1.0b

Counts

2 → 2

Compiler

Compiled 145 to 102 computations (29.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
9.1b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
11.3b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite114.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1799`
34×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `distribute-lft-out_binary64_1750`
24×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
21×	`add-sqr-sqrt_binary64_1821` `associate-r_binary64_1739`
18×	`associate-/r/_binary64_1745`
16×	`frac-times_binary64_1809`
15×	`add-cube-cbrt_binary64_1834`
14×	`times-frac_binary64_1805`
13×	`pow1_binary64_1860`
11×	`swap-sqr_binary64_1766`
10×	`div-exp_binary64_1850` `prod-exp_binary64_1848` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832` `associate-*l/_binary64_1742`
9×	`associate-l_binary64_1740`
8×	`associate-*r/_binary64_1741`
7×	`associate-/l/_binary64_1746`
6×	`associate-/r*_binary64_1743`
5×	`associate-/l*_binary64_1744`
4×	`add-log-exp_binary64_1838`
3×	`unswap-sqr_binary64_1767` `div-inv_binary64_1796`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870`
1×	`pow2_binary64_1880` `pow-sqr_binary64_1772` `distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `pow-prod-up_binary64_1869` `pow-plus_binary64_1862`

Counts

4 → 158

Calls

4 calls:

29.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
21.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series553.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
192.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
100.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
35.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4982	3959
1	4982	3959

prune663.0ms (7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	8	172

Merged error: 0.0b

Counts

172 → 8

Compiler

Compiled 13891 to 9808 computations (29.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
9.1b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite218.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64_1799`
508×	`times-frac_binary64_1805`
374×	`distribute-lft-out_binary64_1750`
191×	`add-sqr-sqrt_binary64_1821`
182×	`add-cube-cbrt_binary64_1834`
136×	`associate-r_binary64_1739`
34×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
31×	`associate-/l*_binary64_1744`
30×	`associate-/r/_binary64_1745`
20×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
15×	`associate-/r*_binary64_1743` `div-inv_binary64_1796`
14×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
8×	`associate-/l/_binary64_1746`
6×	`pow1_binary64_1860` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
4×	`add-log-exp_binary64_1838` `associate-l_binary64_1740` `frac-times_binary64_1809` `associate-*l/_binary64_1742`
3×	`clear-num_binary64_1798` `unswap-sqr_binary64_1767` `frac-2neg_binary64_1810`
2×	`associate-*r/_binary64_1741`
1×	`*-commutative_binary64_1730` `pow-prod-down_binary64_1870`

Counts

4 → 422

Calls

4 calls:

61.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
44.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
24.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series582.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
208.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
93.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
54.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify158.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4941	12598
1	4941	12598

prune1.1s (11.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	435	7	442

Merged error: 0.0b

Counts

442 → 7

Compiler

Compiled 16525 to 10543 computations (36.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.3b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
9.1b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite205.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

829×	`*-un-lft-identity_binary64_1799`
394×	`times-frac_binary64_1805`
355×	`distribute-lft-out_binary64_1750`
248×	`sqrt-prod_binary64_1815`
224×	`add-sqr-sqrt_binary64_1821`
149×	`add-cube-cbrt_binary64_1834`
127×	`swap-sqr_binary64_1766`
45×	`associate-l_binary64_1740`
42×	`associate-r_binary64_1739`
38×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
16×	`pow1_binary64_1860`
14×	`associate-/l*_binary64_1744`
13×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
12×	`associate-/r/_binary64_1745` `flip3-+_binary64_1802` `flip-+_binary64_1773`
10×	`div-exp_binary64_1850` `unswap-sqr_binary64_1767` `associate-/r*_binary64_1743` `cbrt-undiv_binary64_1833` `frac-times_binary64_1809`
7×	`associate-*r/_binary64_1741`
6×	`div-inv_binary64_1796` `associate-*l/_binary64_1742`
4×	`sqrt-div_binary64_1816` `add-log-exp_binary64_1838` `associate-/l/_binary64_1746` `pow-prod-down_binary64_1870`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `*-commutative_binary64_1730`
1×	`pow2_binary64_1880` `pow-sqr_binary64_1772` `pow-prod-up_binary64_1869` `pow-plus_binary64_1862`

Counts

4 → 405

Calls

4 calls:

62.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
33.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
13.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series435.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
108.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
71.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
61.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

simplify135.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5792	11833

prune989.0ms (10.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	416	8	424

Merged error: 0.0b

Counts

424 → 8

Compiler

Compiled 15715 to 10577 computations (32.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
0.6b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
9.1b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite371.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

821×	`*-un-lft-identity_binary64_1799`
550×	`times-frac_binary64_1805`
365×	`distribute-lft-out_binary64_1750`
203×	`add-sqr-sqrt_binary64_1821`
194×	`add-cube-cbrt_binary64_1834`
136×	`associate-r_binary64_1739`
82×	`add-exp-log_binary64_1837`
52×	`add-cbrt-cube_binary64_1835` `associate-/r/_binary64_1745`
44×	`div-exp_binary64_1850`
34×	`associate-/l*_binary64_1744`
26×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
25×	`cbrt-undiv_binary64_1833`
20×	`associate-/r*_binary64_1743`
19×	`div-inv_binary64_1796`
15×	`prod-exp_binary64_1848`
12×	`frac-times_binary64_1809` `associate-*l/_binary64_1742`
9×	`cbrt-unprod_binary64_1832`
7×	`pow1_binary64_1860`
6×	`associate-*r/_binary64_1741`
5×	`rec-exp_binary64_1849` `1-exp_binary64_1843`
4×	`add-log-exp_binary64_1838` `associate-l_binary64_1740`
3×	`clear-num_binary64_1798` `unswap-sqr_binary64_1767` `frac-2neg_binary64_1810` `associate-/l/_binary64_1746`
1×	`pow-flip_binary64_1873` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `inv-pow_binary64_1884`

Counts

4 → 469

Calls

4 calls:

73.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
64.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
61.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
35.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

series709.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
211.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
187.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
94.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

simplify187.0ms (2%)

Algorithm

1×	egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4979	15594
1	4979	15594

prune1.4s (14.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	481	8	489

Merged error: 0.0b

Counts

489 → 8

Compiler

Compiled 17839 to 11708 computations (34.4% saved)

regimes46.0ms (0.5%)

Compiler: Compiled 516 to 384 computations (25.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample1.0s (10.7%)

Algorithm

1×

intervals

Results

487.0ms	8000×	body	128	valid
141.0ms	8000×	pre	128	true

Compiler

Compiled 323 to 237 computations (26.6% saved)

Details

analyze5.0ms (0.1%)

sample33.0ms (0.3%)

simplify425.0ms (4.5%)

prune10.0ms (0.1%)

localize12.0ms (0.1%)

rewrite114.0ms (1.2%)

series553.0ms (5.8%)

simplify85.0ms (0.9%)

prune663.0ms (7%)

localize14.0ms (0.2%)

rewrite218.0ms (2.3%)

series582.0ms (6.1%)

simplify158.0ms (1.7%)

prune1.1s (11.7%)

localize17.0ms (0.2%)

rewrite205.0ms (2.2%)

series435.0ms (4.6%)

simplify135.0ms (1.4%)

prune989.0ms (10.4%)

localize13.0ms (0.1%)

rewrite371.0ms (3.9%)

series709.0ms (7.5%)

simplify187.0ms (2%)

prune1.4s (14.7%)

regimes46.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (10.7%)

Profiling