Details

sample113.0ms

Algorithm

intervals

Results

53.0ms	896×	body	80	nan
23.0ms	302×	body	80	valid

simplify2.1s

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	1129	20
7	1913	20
8	4184	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

localize12.0ms

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)))))

rewrite52.0ms

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))))
16.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series59.0ms

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))))
26.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify888.0ms

Counts

126 → 126

Iterations

Useful iterations: done (876.0ms)

Iter	Nodes	Cost
0	355	2797
1	1014	2683
2	4054	2492
done	5000	2491

prune384.0ms

Filtered

109 candidates to 126 candidates (-15.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	6	127

Merged error: 0.0b

Counts

127 → 6

localize11.0ms

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)))))

rewrite45.0ms

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:

11.0ms	(* 9.0 (- a (/ 1.0 3.0)))
12.0ms	(* (- 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)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 9.0 (- a (/ 1.0 3.0)))
17.0ms	(* (- 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)))))

simplify750.0ms

Counts

116 → 116

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	301	2338
1	839	2260
2	3292	2075
done	5000	2071

prune267.0ms

Filtered

93 candidates to 116 candidates (-24.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 0.0b

Counts

122 → 5

localize13.0ms

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))))

rewrite71.0ms

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)))))))
19.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series46.0ms

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))))

simplify380.0ms

Counts

322 → 322

Iterations

Useful iterations: done (366.0ms)

Iter	Nodes	Cost
0	530	8026
1	1358	7521
done	5000	7365

prune725.0ms

Filtered

190 candidates to 322 candidates (-69.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	320	2	322
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	322	5	327

Merged error: 0.0b

Counts

327 → 5

localize17.0ms

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))))))))

rewrite92.0ms

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)))))))
19.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
22.0ms	(* (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))))))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
39.0ms	(* (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))))))))

simplify434.0ms

Counts

365 → 365

Iterations

Useful iterations: done (416.0ms)

Iter	Nodes	Cost
0	602	10998
1	1596	10028
done	5002	9854

prune1.3s

Filtered

226 candidates to 365 candidates (-61.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	363	2	365
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	364	6	370

Merged error: 0b

Counts

370 → 6

regimes166.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	17	20
done	17	20

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	26832×	body	80	nan
596.0ms	9184×	body	80	valid

Details

sample113.0ms

simplify2.1s

prune11.0ms

localize12.0ms

rewrite52.0ms

series59.0ms

simplify888.0ms

prune384.0ms

localize11.0ms

rewrite45.0ms

series46.0ms

simplify750.0ms

prune267.0ms

localize13.0ms

rewrite71.0ms

series46.0ms

simplify380.0ms

prune725.0ms

localize17.0ms

rewrite92.0ms

series83.0ms

simplify434.0ms

prune1.3s

regimes166.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling