Details

sample68.0ms

Algorithm

intervals

Results

28.0ms	907×	body	80	nan
10.0ms	302×	body	80	valid

simplify4.8s

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	1851	20
8	3925	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))))

rewrite85.0ms

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:

30.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
35.0ms	(* (/ 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))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
200.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
157.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
79.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.1s

Counts

126 → 126

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	303	2615
1	822	2480
2	2974	2274
done	5001	2268

prune391.0ms

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))

rewrite167.0ms

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)
8.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
110.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series620.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
153.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
81.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
181.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify888.0ms

Counts

123 → 123

Iterations

Useful iterations: done (883.0ms)

Iter	Nodes	Cost
0	291	2353
1	754	2261
2	2563	2003
done	5001	1995

prune378.0ms

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))))

rewrite183.0ms

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:

110.0ms	(* (* (- 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)))))
53.0ms	(* (- 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))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
162.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
138.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
81.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify915.0ms

Counts

127 → 127

Iterations

Useful iterations: done (903.0ms)

Iter	Nodes	Cost
0	287	2571
1	728	2467
2	2680	2183
done	5000	2175

prune361.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

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))))

rewrite104.0ms

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:

22.0ms	(* 9.0 (- a (/ 1.0 3.0)))
18.0ms	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
54.0ms	(* (/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 9.0 (- a (/ 1.0 3.0)))
142.0ms	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
177.0ms	(* (/ (* (- 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))))

simplify794.0ms

Counts

109 → 109

Iterations

Useful iterations: done (790.0ms)

Iter	Nodes	Cost
0	246	1965
1	661	1867
2	2298	1613
done	5000	1607

prune287.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes82.0ms

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

871.0ms	27466×	body	80	nan
324.0ms	9173×	body	80	valid