Details

sample83.0ms

Algorithm

intervals

Results

35.0ms	838×	body	80	nan
13.0ms	292×	body	80	valid

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	76	19
3	206	19
4	503	19
5	992	19
6	2080	19
7	3449	19
done	5000	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
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)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite285.0ms

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×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `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 → 122

Calls

4 calls:

92.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
109.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
17.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
62.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
319.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
205.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
101.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.4s

Counts

134 → 134

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	311	2723
1	860	2576
2	3111	2342
done	5001	2340

prune509.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.0b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
85×	`add-cube-cbrt`
78×	`prod-diff`
68×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`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`

Counts

4 → 190

Calls

4 calls:

71.0ms	(* 9.0 (- a (/ 1.0 3.0)))
83.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
18.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
61.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* 9.0 (- a (/ 1.0 3.0)))
197.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
220.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
106.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.6s

Counts

202 → 202

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	495	5689
1	1127	5171
2	3647	3969
done	5000	3617

prune574.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(* (- 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))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

403×	`times-frac`
310×	`add-sqr-sqrt`
234×	`sqrt-prod`
232×	`*-un-lft-identity`
182×	`add-cube-cbrt`
50×	`difference-of-squares`
25×	`distribute-lft-out--`
22×	`associate-/l*`
11×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`flip3--` `flip--`
4×	`frac-times` `sqrt-div`
3×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `div-exp` `associate-r` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

3 → 301

Calls

3 calls:

27.0ms	(sqrt (- a (/ 1.0 3.0)))
77.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
50.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series550.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(sqrt (- a (/ 1.0 3.0)))
222.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
276.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify2.1s

Counts

310 → 310

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	497	7824
1	1245	7159
2	3795	6954
done	5000	6952

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0b	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
78×	`prod-diff`
68×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
17×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
10×	`associate-*r/`
9×	`associate-l`
7×	`associate-r` `div-inv`
6×	`prod-exp` `cbrt-unprod`
5×	`flip3--` `pow-prod-down` `sqrt-prod` `flip--`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `sqrt-pow1` `div-exp` `associate-l/` `associate-/r/` `-commutative` `distribute-lft-out--`
1×	`frac-2neg` `pow1/2` `clear-num` `unswap-sqr`

Counts

4 → 187

Calls

4 calls:

101.0ms	(* 9.0 (- a (/ 1.0 3.0)))
23.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
46.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
208.0ms	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

series756.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 9.0 (- a (/ 1.0 3.0)))
269.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
135.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
287.0ms	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

simplify3.1s

Counts

199 → 199

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	492	5414
1	1070	4914
2	3195	3723
done	5001	3200

prune576.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.8s	27510×	body	80	nan
921.0ms	9104×	body	80	valid