Details

analyze75.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	10×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify215.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune5.0ms (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: 0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2120`
23×	`*-un-lft-identity_binary64_2099`
17×	`add-cube-cbrt_binary64_2131`
12×	`times-frac_binary64_2105`
11×	`pow1_binary64_2157`
10×	`associate-l_binary64_2042` `add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
8×	`associate-*l/_binary64_2044`
7×	`associate-r_binary64_2041`
6×	`flip3--_binary64_2103` `flip--_binary64_2074`
5×	`sqrt-prod_binary64_2114`
4×	`add-log-exp_binary64_2135` `associate-/r*_binary64_2045` `sqrt-div_binary64_2115` `frac-times_binary64_2109`
3×	`flip3-+_binary64_2102` `pow-prod-down_binary64_2167` `associate-/l*_binary64_2046` `flip-+_binary64_2073`
2×	`difference-of-squares_binary64_2068` `associate-r/_binary64_2043` `-commutative_binary64_2032` `associate-/r/_binary64_2047` `prod-exp_binary64_2145` `unswap-sqr_binary64_2067` `distribute-lft-out--_binary64_2053` `sqrt-pow1_binary64_2116` `cbrt-unprod_binary64_2129`
1×	`distribute-lft-out_binary64_2052` `cbrt-undiv_binary64_2130` `distribute-rgt-in_binary64_2051` `distribute-lft-in_binary64_2050` `div-exp_binary64_2147` `frac-2neg_binary64_2110` `pow1/2_binary64_2176` `clear-num_binary64_2098` `div-inv_binary64_2096`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series301.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
81.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
43.0ms	(*.f64 (-.f64 a 1/3) 9)
35.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5372	2236

prune163.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.0b

Counts

113 → 5

Compiler

Compiled 2567 to 1993 computations (22.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
10.4b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_2120`
28×	`*-un-lft-identity_binary64_2099`
25×	`times-frac_binary64_2105`
24×	`add-cube-cbrt_binary64_2131`
21×	`associate-r_binary64_2041`
13×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
11×	`pow1_binary64_2157`
10×	`associate-l_binary64_2042` `associate-*l/_binary64_2044`
8×	`sqrt-prod_binary64_2114`
6×	`sqrt-div_binary64_2115` `flip3--_binary64_2103` `flip--_binary64_2074`
4×	`associate-/r/_binary64_2047` `add-log-exp_binary64_2135` `associate-/r*_binary64_2045`
3×	`prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `associate-/l*_binary64_2046` `cbrt-unprod_binary64_2129`
2×	`difference-of-squares_binary64_2068` `cbrt-undiv_binary64_2130` `*-commutative_binary64_2032` `div-exp_binary64_2147` `frac-times_binary64_2109` `div-inv_binary64_2096` `distribute-lft-out--_binary64_2053` `sqrt-pow1_binary64_2116`
1×	`associate-*r/_binary64_2043` `frac-2neg_binary64_2110` `pow1/2_binary64_2176` `clear-num_binary64_2098`

Counts

4 → 111

Calls

4 calls:

17.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series325.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
111.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
42.0ms	(*.f64 (-.f64 a 1/3) 9)
35.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4933	2404
1	4933	2404

prune166.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Merged error: 0b

Counts

128 → 5

Compiler

Compiled 3027 to 2244 computations (25.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

rewrite139.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64_2105`
248×	`add-sqr-sqrt_binary64_2120`
247×	`*-un-lft-identity_binary64_2099`
223×	`sqrt-prod_binary64_2114`
191×	`add-cube-cbrt_binary64_2131`
33×	`associate-/l*_binary64_2046`
27×	`difference-of-squares_binary64_2068` `distribute-lft-out--_binary64_2053`
18×	`sqrt-div_binary64_2115`
16×	`associate-/r/_binary64_2047`
14×	`associate-/r*_binary64_2045`
13×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
12×	`flip3--_binary64_2103` `flip--_binary64_2074`
9×	`div-inv_binary64_2096`
7×	`pow1_binary64_2157`
5×	`associate-l_binary64_2042`
4×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `add-log-exp_binary64_2135` `associate-r_binary64_2041` `frac-times_binary64_2109`
3×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
2×	`associate-r/_binary64_2043` `associate-l/_binary64_2044` `frac-2neg_binary64_2110` `clear-num_binary64_2098`
1×	`distribute-lft-out_binary64_2052` `distribute-rgt-in_binary64_2051` `*-commutative_binary64_2032` `distribute-lft-in_binary64_2050` `associate-/l/_binary64_2048` `prod-exp_binary64_2145` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `sqrt-pow1_binary64_2116` `cbrt-unprod_binary64_2129`

Counts

4 → 328

Calls

4 calls:

61.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
16.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series352.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
105.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
90.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
29.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify147.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4928	9000
1	4928	9000

prune682.0ms (12.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	340	5	345

Merged error: 0b

Counts

345 → 5

Compiler

Compiled 8710 to 6561 computations (24.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
3.8b	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))

rewrite100.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`add-sqr-sqrt_binary64_2120`
103×	`times-frac_binary64_2105`
86×	`*-un-lft-identity_binary64_2099`
78×	`sqrt-prod_binary64_2114`
56×	`add-cube-cbrt_binary64_2131`
41×	`associate-l_binary64_2042`
27×	`associate-r_binary64_2041`
18×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
16×	`sqrt-div_binary64_2115`
15×	`difference-of-squares_binary64_2068` `distribute-lft-out--_binary64_2053`
12×	`pow1_binary64_2157`
11×	`associate-*l/_binary64_2044`
9×	`unswap-sqr_binary64_2067`
7×	`associate-/r*_binary64_2045`
6×	`associate-/r/_binary64_2047` `flip3--_binary64_2103` `flip--_binary64_2074`
5×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `associate-/l*_binary64_2046`
4×	`prod-exp_binary64_2145` `add-log-exp_binary64_2135` `sqrt-pow1_binary64_2116` `cbrt-unprod_binary64_2129`
3×	`pow-prod-down_binary64_2167` `div-inv_binary64_2096`
2×	`associate-/l/_binary64_2048` `pow1/2_binary64_2176`
1×	`associate-r/_binary64_2043` `-commutative_binary64_2032` `frac-2neg_binary64_2110` `div-sub_binary64_2104` `clear-num_binary64_2098` `frac-times_binary64_2109`

Counts

4 → 187

Calls

4 calls:

47.0ms	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
14.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series349.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
103.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
32.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
32.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5198	5957

prune450.0ms (8.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	199	5	204

Merged error: 0b

Counts

204 → 5

Compiler

Compiled 6941 to 5544 computations (20.1% saved)

regimes276.0ms (5%)

Compiler: Compiled 3030 to 2662 computations (12.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample1.4s (25%)

Algorithm

1×

intervals

Results

475.0ms	8000×	body	128	valid
17.0ms	254×	body	128	invalid
17.0ms	266×	body	128	nan

Compiler

Compiled 781 to 687 computations (12% saved)

Details

analyze75.0ms (1.4%)

sample27.0ms (0.5%)

simplify215.0ms (3.9%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite47.0ms (0.9%)

series301.0ms (5.5%)

simplify54.0ms (1%)

prune163.0ms (3%)

localize9.0ms (0.2%)

rewrite50.0ms (0.9%)

series325.0ms (5.9%)

simplify66.0ms (1.2%)

prune166.0ms (3%)

localize9.0ms (0.2%)

rewrite139.0ms (2.5%)

series352.0ms (6.4%)

simplify147.0ms (2.7%)

prune682.0ms (12.4%)

localize11.0ms (0.2%)

rewrite100.0ms (1.8%)

series349.0ms (6.3%)

simplify90.0ms (1.6%)

prune450.0ms (8.2%)

regimes276.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (25%)

Profiling