Details

sample58.0ms

Algorithm

intervals

Results

23.0ms	759×	body	80	nan
12.0ms	280×	body	80	valid

simplify4.2s

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	3926	20
done	5000	20

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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))))

rewrite88.0ms

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:

29.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
39.0ms	(* (/ 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))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
195.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
156.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.3s

Counts

126 → 126

Iterations

Useful iterations: done (1.3s)

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

prune389.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

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

rewrite73.0ms

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:

23.0ms	(* 9.0 (- a (/ 1.0 3.0)))
28.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
12.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 9.0 (- a (/ 1.0 3.0)))
133.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
165.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
81.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify784.0ms

Counts

116 → 116

Iterations

Useful iterations: done (773.0ms)

Iter	Nodes	Cost
0	271	2223
1	721	2134
2	2561	1938
done	5000	1934

prune343.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
102×	`times-frac`
76×	`*-un-lft-identity`
62×	`add-exp-log` `sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-r`
38×	`add-cbrt-cube`
29×	`associate-l`
26×	`prod-exp`
17×	`div-exp`
16×	`difference-of-squares` `unswap-sqr`
14×	`cbrt-unprod`
13×	`pow1`
9×	`cbrt-undiv` `associate-/r*`
8×	`distribute-lft-out--`
7×	`associate-*l/`
6×	`frac-times`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`rec-exp` `sqrt-div` `1-exp` `associate-*r/` `associate-/r/` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 209

Calls

4 calls:

28.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
59.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
13.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
53.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
231.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
85.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
196.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

simplify1.7s

Counts

221 → 221

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	415	4792
1	1176	4194
2	4035	3732
done	5000	3726

prune607.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0))) (sqrt 9.0))
0.3b	(* (/ (/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0))) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))))
0.3b	(/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0)))
0.3b	(/ (cbrt 1.0) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

12828×	`times-frac`
7388×	`*-un-lft-identity`
6090×	`add-sqr-sqrt`
5876×	`sqrt-prod`
5296×	`add-cube-cbrt`
4450×	`cbrt-prod`
1906×	`associate-l`
1020×	`distribute-lft-out`
329×	`associate-/l*`
115×	`unswap-sqr`
103×	`div-inv`
90×	`associate-r`
78×	`difference-of-squares`
72×	`associate-/r*`
52×	`add-exp-log`
35×	`add-cbrt-cube`
26×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
18×	`associate-/r/`
8×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`sqrt-div` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 4884

Calls

4 calls:

142.0ms	(/ (/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0))) (sqrt 9.0))
2.3s	(* (/ (/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0))) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))))
38.0ms	(/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0)))
25.0ms	(/ (cbrt 1.0) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))))

series4.5s

Counts

4 → 12

Calls

4 calls:

539.0ms	(/ (/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0))) (sqrt 9.0))
2.9s	(* (/ (/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0))) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))))
455.0ms	(/ (cbrt 1.0) (/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (cbrt 1.0)))
598.0ms	(/ (cbrt 1.0) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))))

simplify1.4s

Counts

4896 → 4896

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	2910	171863
done	5000	171779

prune22.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	22	23
done	22	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

823.0ms	26969×	body	80	nan
309.0ms	9094×	body	80	valid