Details

sample63.0ms

Algorithm

intervals

Results

27.0ms	907×	body	80	nan
10.0ms	302×	body	80	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	70	20
3	172	20
4	352	20
5	667	20
6	1102	20
7	1857	20
8	3927	20
done	5000	20

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite95.0ms

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:

31.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
38.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
12.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
196.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
147.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify942.0ms

Counts

126 → 126

Iterations

Useful iterations: done (938.0ms)

Iter	Nodes	Cost
0	303	2615
1	822	2480
2	3050	2274
done	5000	2268

prune384.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
7.4b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

38.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
116.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series591.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
152.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
168.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify775.0ms

Counts

123 → 123

Iterations

Useful iterations: done (771.0ms)

Iter	Nodes	Cost
0	291	2353
1	754	2261
2	2622	2003
done	5001	1995

prune357.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
9×	`associate-*l/`
8×	`associate-*r/` `sqrt-prod`
7×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
6×	`sqrt-div`
5×	`pow-prod-down`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`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:

118.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
56.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
151.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
137.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify786.0ms

Counts

127 → 127

Iterations

Useful iterations: done (781.0ms)

Iter	Nodes	Cost
0	287	2571
1	728	2467
2	2762	2183
done	5000	2175

prune367.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

24.0ms	(* 9.0 (- a (/ 1.0 3.0)))
18.0ms	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
63.0ms	(* (/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 9.0 (- a (/ 1.0 3.0)))
144.0ms	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
175.0ms	(* (/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify739.0ms

Counts

109 → 109

Iterations

Useful iterations: done (735.0ms)

Iter	Nodes	Cost
0	246	1965
1	661	1867
2	2444	1613
done	5001	1607

prune290.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes79.0ms

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	26
1	17	26
done	17	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

861.0ms	27466×	body	80	nan
323.0ms	9173×	body	80	valid