Details

sample106.0ms

Algorithm

intervals

Results

25.0ms	249×	body	80	nan
22.0ms	117×	body	320	valid
16.0ms	505×	pre	80	true
11.0ms	92×	body	160	valid
5.0ms	20×	body	640	valid
2.0ms	27×	body	80	valid

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	88	16
5	96	16
done	96	16

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
28.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 73

Calls

4 calls:

17.0ms	(- (* b b) (* (* 3.0 a) c))
110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
26.0ms	(* (* 3.0 a) c)
56.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* b b) (* (* 3.0 a) c))
203.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(* (* 3.0 a) c)
143.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.6s

Counts

85 → 85

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	1437
1	410	1361
2	1549	1139
done	5001	1125

prune271.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a c) 3.0)
0.2b	(* 3.0 (* a c))
0.3b	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
0.4b	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/r/`
4×	`associate-r` `associate-l` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 157

Calls

4 calls:

19.0ms	(* (* a c) 3.0)
20.0ms	(* 3.0 (* a c))
145.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
183.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (* 3.0 a))

series543.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* a c) 3.0)
23.0ms	(* 3.0 (* a c))
286.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
202.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (* 3.0 a))

simplify2.2s

Counts

169 → 169

Iterations

Useful iterations: 2 (748.0ms)

Iter	Nodes	Cost
0	242	4718
1	605	4240
2	2435	3862
done	5001	3862

prune545.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(/ (/ 1 1) (/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))))
0.3b	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
0.4b	(/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

719×	`times-frac`
335×	`add-exp-log`
258×	`add-sqr-sqrt` `*-un-lft-identity`
214×	`div-exp`
186×	`add-cube-cbrt`
143×	`add-cbrt-cube`
86×	`prod-exp`
72×	`cbrt-undiv`
52×	`div-inv`
50×	`associate-/r/`
45×	`1-exp`
38×	`associate-/r*`
36×	`cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
18×	`rec-exp` `distribute-rgt-neg-in` `sqrt-prod`
17×	`flip3--` `flip--`
15×	`associate-/l*`
9×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num`
1×	`associate-l` `*-commutative` `associate-/l/`

Counts

4 → 463

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
104.0ms	(/ (/ 1 1) (/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))))
89.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
125.0ms	(/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 3.0 a) c)
271.0ms	(/ (/ 1 1) (/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))))
259.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
144.0ms	(/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))))

simplify3.5s

Counts

475 → 475

Iterations

Useful iterations: 2 (1.8s)

Iter	Nodes	Cost
0	668	19625
1	1669	16561
2	4346	14431
done	5000	14431

prune765.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (pow b 2) (* 3.0 (* a c))))
0.1b	(- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))
0.1b	(- (pow b 2) (* 3.0 (* a c)))
0.2b	(* 3.0 (* a c))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `*-commutative`

Counts

4 → 63

Calls

4 calls:

15.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))
40.0ms	(- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))
19.0ms	(- (pow b 2) (* 3.0 (* a c)))
31.0ms	(* 3.0 (* a c))

series304.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (- (pow b 2) (* 3.0 (* a c))))
105.0ms	(- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))
65.0ms	(- (pow b 2) (* 3.0 (* a c)))
22.0ms	(* 3.0 (* a c))

simplify3.4s

Counts

75 → 75

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	121	1080
1	280	972
2	882	902
3	3348	888
done	5000	886

prune366.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	25
1	25	23
done	25	23

end0.0ms

sample4.3s

Algorithm

intervals

Results

978.0ms	3641×	body	320	valid
809.0ms	16012×	pre	80	true
753.0ms	8012×	body	80	nan
506.0ms	896×	body	80	valid
454.0ms	2959×	body	160	valid
179.0ms	504×	body	640	valid