Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	189×	body	128	valid
5.0ms	35×	body	1024	valid
4.0ms	256×	pre	128	true
2.0ms	22×	body	512	valid
1.0ms	3×	body	2048	valid
0.0ms	7×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify310.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	5139	19

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1799`
26×	`add-sqr-sqrt_binary64_1821`
25×	`times-frac_binary64_1805`
19×	`distribute-lft-out_binary64_1750`
14×	`add-cube-cbrt_binary64_1834`
6×	`difference-of-squares_binary64_1768` `distribute-lft-out--_binary64_1751`
5×	`associate-/l_binary64_1744` `associate-/r_binary64_1743`
4×	`add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
2×	`pow1_binary64_1860` `div-sub_binary64_1804` `associate-/r/_binary64_1745` `associate-/l/_binary64_1746` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `div-exp_binary64_1850` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796` `associate-+l-_binary64_1734`

Counts

2 → 65

Calls

2 calls:

20.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series158.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

90.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
68.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5220	1488

prune251.0ms (5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 16.1b

Counts

72 → 11

Compiler

Compiled 5079 to 3389 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite86.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`*-un-lft-identity_binary64_1799`
68×	`add-sqr-sqrt_binary64_1821`
58×	`times-frac_binary64_1805`
37×	`add-cube-cbrt_binary64_1834`
24×	`distribute-lft-out_binary64_1750`
13×	`associate-/l_binary64_1744` `associate-/r_binary64_1743` `distribute-lft-out--_binary64_1751`
12×	`difference-of-squares_binary64_1768`
10×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
6×	`add-log-exp_binary64_1838`
4×	`pow1_binary64_1860` `associate-/r/_binary64_1745` `associate-/l/_binary64_1746`
3×	`clear-num_binary64_1798` `div-exp_binary64_1850` `frac-2neg_binary64_1810` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796` `cancel-sign-sub-inv_binary64_1765`
2×	`difference-of-sqr-1_binary64_1769` `frac-sub_binary64_1808` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `diff-log_binary64_1891`

Counts

4 → 143

Calls

4 calls:

38.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series357.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
109.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
67.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
62.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5352	3804

prune708.0ms (14%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	147	8	155
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	158	8	166

Merged error: 2.9b

Counts

166 → 8

Compiler

Compiled 14692 to 10048 computations (31.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
1.2b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite64.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64_1799`
50×	`add-sqr-sqrt_binary64_1821`
36×	`times-frac_binary64_1805`
28×	`add-cube-cbrt_binary64_1834`
24×	`distribute-lft-out_binary64_1750`
11×	`log-pow_binary64_1888`
10×	`associate-/r*_binary64_1743` `exp-prod_binary64_1851`
8×	`add-cbrt-cube_binary64_1835` `difference-of-squares_binary64_1768` `add-exp-log_binary64_1837`
7×	`log-prod_binary64_1885`
6×	`associate-/l*_binary64_1744` `add-log-exp_binary64_1838` `cancel-sign-sub-inv_binary64_1765`
5×	`pow1_binary64_1860`
4×	`exp-sum_binary64_1845` `associate-/r/_binary64_1745` `difference-of-sqr-1_binary64_1769`
2×	`sub-neg_binary64_1792` `clear-num_binary64_1798` `div-exp_binary64_1850` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796` `flip3-+_binary64_1802` `distribute-lft-out--_binary64_1751` `flip-+_binary64_1773`
1×	`exp-diff_binary64_1847` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `rem-log-exp_binary64_1840` `log-div_binary64_1886`

Counts

4 → 122

Calls

4 calls:

18.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series403.0ms (8%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
108.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
62.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
53.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5005	2196

prune182.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	133	9	142

Merged error: 2.9b

Counts

142 → 9

Compiler

Compiled 4115 to 2589 computations (37.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.4b	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.5b	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite106.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`*-un-lft-identity_binary64_1799`
126×	`add-sqr-sqrt_binary64_1821`
121×	`times-frac_binary64_1805`
81×	`sqrt-prod_binary64_1815`
69×	`add-cube-cbrt_binary64_1834`
42×	`distribute-lft-out_binary64_1750`
32×	`add-exp-log_binary64_1837`
30×	`associate-l_binary64_1740` `associate-r_binary64_1739`
20×	`add-cbrt-cube_binary64_1835`
16×	`associate-/r*_binary64_1743`
15×	`unswap-sqr_binary64_1767`
11×	`div-exp_binary64_1850`
8×	`pow1_binary64_1860` `sqrt-div_binary64_1816` `prod-exp_binary64_1848` `associate-/r/_binary64_1745`
6×	`associate-/l*_binary64_1744` `add-log-exp_binary64_1838` `cbrt-undiv_binary64_1833`
4×	`difference-of-squares_binary64_1768` `cbrt-unprod_binary64_1832` `div-inv_binary64_1796` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`rec-exp_binary64_1849` `pow-flip_binary64_1873` `1-exp_binary64_1843` `cancel-sign-sub-inv_binary64_1765`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `difference-of-sqr-1_binary64_1769`
1×	`sub-neg_binary64_1792` `pow1/2_binary64_1879` `associate-r/_binary64_1741` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `sqrt-pow1_binary64_1817` `-commutative_binary64_1730` `pow-prod-down_binary64_1870` `distribute-lft-out--_binary64_1751` `inv-pow_binary64_1884` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 224

Calls

4 calls:

38.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
9.0ms	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

series373.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
96.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
85.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
69.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4969	4832
1	4969	4832

prune489.0ms (9.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	232	4	236
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	235	10	245

Merged error: 2.9b

Counts

245 → 10

Compiler

Compiled 9859 to 6361 computations (35.5% saved)

regimes72.0ms (1.4%)

Compiler: Compiled 618 to 466 computations (24.6% saved)

bsearch20.0ms (0.4%)

Steps

Iters	Range		Point
7	1273.5860333074334	282484.52375809825	274462.6546204756

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	198	91
1	198	91

end0.0ms (0%)

sample1.0s (20.6%)

Algorithm

1×

intervals

Results

206.0ms	5968×	body	128	valid
144.0ms	8000×	pre	128	true
133.0ms	1019×	body	1024	valid
58.0ms	601×	body	512	valid
21.0ms	307×	body	256	valid
17.0ms	105×	body	2048	valid

Compiler

Compiled 387 to 290 computations (25.1% saved)

Details

analyze3.0ms (0.1%)

sample26.0ms (0.5%)

simplify310.0ms (6.1%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite38.0ms (0.7%)

series158.0ms (3.1%)

simplify63.0ms (1.3%)

prune251.0ms (5%)

localize12.0ms (0.2%)

rewrite86.0ms (1.7%)

series357.0ms (7.1%)

simplify77.0ms (1.5%)

prune708.0ms (14%)

localize15.0ms (0.3%)

rewrite64.0ms (1.3%)

series403.0ms (8%)

simplify52.0ms (1%)

prune182.0ms (3.6%)

localize18.0ms (0.4%)

rewrite106.0ms (2.1%)

series373.0ms (7.4%)

simplify109.0ms (2.1%)

prune489.0ms (9.7%)

regimes72.0ms (1.4%)

bsearch20.0ms (0.4%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample1.0s (20.6%)

Profiling