Details

analyze80.0ms (2%)

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)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid
0.0ms	7×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune6.0ms (0.2%)

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 82 to 77 computations (6.1% saved)

localize8.0ms (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)))))
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
8×	`associate-*l/_binary64`
7×	`associate-r_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`sqrt-prod_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `frac-times_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 99

Calls

4 calls:

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

series281.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.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)))))
39.0ms	(*.f64 (-.f64 a 1/3) 9)
37.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5477	2236

prune509.0ms (12.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 0b

Counts

113 → 8

Compiler

Compiled 8459 to 7172 computations (15.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.8b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite55.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `associate-*l/_binary64`
8×	`sqrt-prod_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 111

Calls

4 calls:

22.0ms	(.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)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series329.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
112.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
47.0ms	(*.f64 (-.f64 a 1/3) 9)
43.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5021	2404

prune191.0ms (4.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	123	8	131

Merged error: 0b

Counts

131 → 8

Compiler

Compiled 3493 to 2647 computations (24.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.4b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.5b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite91.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
110×	`times-frac_binary64`
75×	`sqrt-prod_binary64`
59×	`add-cube-cbrt_binary64`
46×	`associate-l_binary64`
29×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`add-log-exp_binary64` `unswap-sqr_binary64`
8×	`associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`frac-add_binary64` `sqrt-div_binary64`
5×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-+l+_binary64` `associate-/r/_binary64` `prod-exp_binary64`
3×	`associate-r/_binary64` `cancel-sign-sub-inv_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `pow-div_binary64` `sqrt-pow1_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-+l-_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 209

Calls

4 calls:

39.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
11.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series270.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
88.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
36.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
28.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify110.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4927	4585
1	4927	4585

prune374.0ms (9.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	5	1	6
Picked	0	1	1
Done	1	0	1
Total	225	4	229

Merged error: 0b

Counts

229 → 4

Compiler

Compiled 5800 to 4500 computations (22.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
13×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64`
8×	`associate-l_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `associate-+l+_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

11.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
10.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))
9.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series292.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))
87.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
70.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
30.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5023	1975

prune139.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	105	4	109

Merged error: 0b

Counts

109 → 4

Compiler

Compiled 2304 to 1754 computations (23.9% saved)

regimes24.0ms (0.6%)

Compiler: Compiled 120 to 112 computations (6.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	18
1	23	18

end0.0ms (0%)

sample776.0ms (19.7%)

Algorithm

1×

intervals

Results

483.0ms	8000×	body	128	valid
18.0ms	274×	body	128	invalid
15.0ms	267×	body	128	nan

Compiler

Compiled 91 to 85 computations (6.6% saved)

Details

analyze80.0ms (2%)

sample24.0ms (0.6%)

simplify67.0ms (1.7%)

prune6.0ms (0.2%)

localize8.0ms (0.2%)

rewrite52.0ms (1.3%)

series281.0ms (7.1%)

simplify51.0ms (1.3%)

prune509.0ms (12.9%)

localize9.0ms (0.2%)

rewrite55.0ms (1.4%)

series329.0ms (8.4%)

simplify70.0ms (1.8%)

prune191.0ms (4.9%)

localize9.0ms (0.2%)

rewrite91.0ms (2.3%)

series270.0ms (6.8%)

simplify110.0ms (2.8%)

prune374.0ms (9.5%)

localize11.0ms (0.3%)

rewrite41.0ms (1.1%)

series292.0ms (7.4%)

simplify64.0ms (1.6%)

prune139.0ms (3.5%)

regimes24.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample776.0ms (19.7%)

Profiling