Details

sample108.0ms

Algorithm

intervals

Results

51.0ms	896×	body	80	nan
22.0ms	302×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	70	20
3	174	20
4	361	20
5	676	20
6	1114	20
7	1879	20
8	4117	20
done	5000	20

prune11.0ms

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 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

12.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
15.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
25.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify877.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (306.0ms)

Iter	Nodes	Cost
0	355	2797
1	1014	2674
2	4118	2482
done	5000	2482

prune370.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Merged error: 0.0b

Counts

127 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`sub-neg` `sqrt-pow1` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

10.0ms	(* 9.0 (- a (/ 1.0 3.0)))
11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 9.0 (- a (/ 1.0 3.0)))
16.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify761.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (245.0ms)

Iter	Nodes	Cost
0	301	2338
1	839	2257
2	3353	2071
done	5000	2071

prune265.0ms

Filtered

93 candidates to 116 candidates (-24.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ 1.0 3.0))
0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
0.3b	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

404×	`times-frac`
316×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
234×	`sqrt-prod`
183×	`add-cube-cbrt`
52×	`difference-of-squares`
26×	`distribute-lft-out--`
22×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube` `div-inv`
9×	`associate-/r*`
7×	`pow1`
6×	`flip3--` `associate-l` `flip--` `add-log-exp`
4×	`frac-times` `sqrt-div`
3×	`cbrt-undiv` `flip3-+` `div-exp` `associate-r` `flip-+`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

4 → 310

Calls

4 calls:

7.0ms	(- a (/ 1.0 3.0))
7.0ms	(sqrt (- a (/ 1.0 3.0)))
11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
18.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- a (/ 1.0 3.0))
4.0ms	(sqrt (- a (/ 1.0 3.0)))
20.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
19.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify998.0ms

Counts

322 → 322

Iterations

Useful iterations: 2 (412.0ms)

Iter	Nodes	Cost
0	530	8026
1	1358	7517
2	4995	7197
done	5000	7197

prune721.0ms

Filtered

185 candidates to 322 candidates (-74.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	319	3	322
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	321	5	326

Merged error: 0.0b

Counts

326 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
0.3b	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

404×	`times-frac`
321×	`add-sqr-sqrt`
247×	`sqrt-prod`
238×	`*-un-lft-identity`
186×	`add-cube-cbrt`
52×	`difference-of-squares`
46×	`sqrt-div`
32×	`frac-times`
26×	`distribute-lft-out--`
23×	`flip3--` `flip--`
22×	`associate-/l*`
18×	`associate-l`
16×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
12×	`pow1` `flip3-+` `flip-+`
11×	`div-inv`
10×	`associate-*l/`
9×	`associate-/r*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 353

Calls

4 calls:

7.0ms	(sqrt (- a (/ 1.0 3.0)))
13.0ms	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
18.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
21.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
38.0ms	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
19.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
21.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))))

simplify470.0ms

Counts

365 → 365

Iterations

Useful iterations: done (452.0ms)

Iter	Nodes	Cost
0	602	10998
1	1596	10005
done	5001	9707

prune1.0s

Filtered

214 candidates to 365 candidates (-70.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	365	5	370

Merged error: 0b

Counts

370 → 5

regimes157.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	17	21
done	17	21

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.8s	26832×	body	80	nan
564.0ms	9184×	body	80	valid

Details

sample108.0ms

simplify1.5s

prune11.0ms

localize11.0ms

rewrite50.0ms

series58.0ms

simplify877.0ms

prune370.0ms

localize12.0ms

rewrite43.0ms

series45.0ms

simplify761.0ms

prune265.0ms

localize12.0ms

rewrite69.0ms

series45.0ms

simplify998.0ms

prune721.0ms

localize16.0ms

rewrite91.0ms

series82.0ms

simplify470.0ms

prune1.0s

regimes157.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling