Details

sample109.0ms

Algorithm

intervals

Results

41.0ms	883×	body	80	nan
27.0ms	290×	body	80	valid

simplify9.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	72	20
3	188	20
4	417	20
5	772	20
6	1496	20
7	2490	20
8	3402	20
9	4724	20
done	5000	20

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

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

rewrite202.0ms

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:

76.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
12.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
82.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
28.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series665.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
81.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
242.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
210.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.0s

Counts

126 → 126

Iterations

Useful iterations: 2 (737.0ms)

Iter	Nodes	Cost
0	303	2615
1	823	2480
2	2960	2274
done	5002	2274

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.2b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.1b	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

rewrite522.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

14.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
127.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
25.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
350.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
270.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
215.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
243.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

simplify2.2s

Counts

127 → 127

Iterations

Useful iterations: 2 (589.0ms)

Iter	Nodes	Cost
0	298	2467
1	787	2371
2	2739	2113
done	5000	2113

prune556.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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)))))
10.1b	(* (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

73.0ms	(* 9.0 (- a (/ 1.0 3.0)))
21.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
256.0ms	(* (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))

series669.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 9.0 (- a (/ 1.0 3.0)))
93.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
232.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
270.0ms	(* (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))

simplify1.6s

Counts

117 → 117

Iterations

Useful iterations: 2 (467.0ms)

Iter	Nodes	Cost
0	271	2084
1	712	2006
2	2492	1794
done	5001	1794

prune456.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ rand (* 1 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
10.1b	(* (* 1.0 (/ rand (* 1 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))) (- a (/ 1.0 3.0)))

rewrite609.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

39.0ms	(* 9.0 (- a (/ 1.0 3.0)))
12.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
42.0ms	(/ rand (* 1 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
512.0ms	(* (* 1.0 (/ rand (* 1 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))) (- a (/ 1.0 3.0)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 9.0 (- a (/ 1.0 3.0)))
81.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
216.0ms	(/ rand (* 1 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
239.0ms	(* (* 1.0 (/ rand (* 1 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))) (- a (/ 1.0 3.0)))

simplify1.9s

Counts

111 → 111

Iterations

Useful iterations: 2 (560.0ms)

Iter	Nodes	Cost
0	276	2137
1	731	1879
2	2614	1631
done	5002	1631

prune396.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	16	28
1	24	26
done	24	26

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.3s	27522×	body	80	nan
1.4s	9155×	body	80	valid