Details

sample49.0ms

Algorithm

intervals

Results

12.0ms	197×	body	80	valid
7.0ms	28×	body	2560	valid
6.0ms	31×	body	1280	valid
3.0ms	77×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

158.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
91.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
102.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	154	1592
1	386	1488
2	1234	1332
3	4639	1324
done	5002	1324

prune361.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

55.0ms	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
74.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
141.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms	(- (* b b) (* (* 4.0 a) c))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts

83 → 83

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	145	1551
1	348	1445
2	1141	1291
3	4485	1287
done	5000	1287

prune324.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

22.0ms	(* (* 4.0 a) c)
72.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 4.0 a) c)
91.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
55.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts

72 → 72

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	120	1001
1	276	903
2	929	825
3	3449	821
done	5000	815

prune255.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.6b	(* (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) (/ 1 (* 2.0 a)))
11.5b	(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
38×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`times-frac`
27×	`add-cbrt-cube`
24×	`add-cube-cbrt`
20×	`prod-exp`
18×	`associate-l`
16×	`div-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r` `distribute-lft-out`
6×	`add-log-exp`
4×	`rec-exp` `1-exp` `associate-/r*` `associate-/r/`
3×	`flip3--` `sqrt-prod` `flip--` `div-inv` `associate-/l*`
2×	`flip3-+` `sub0-neg` `sqrt-div` `distribute-frac-neg` `flip-+` `associate-/l/` `unswap-sqr`
1×	`distribute-lft-neg-out` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

4 → 125

Calls

4 calls:

17.0ms	(- (* b b) (* (* 4.0 a) c))
201.0ms	(* (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) (/ 1 (* 2.0 a)))
52.0ms	(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series733.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b b) (* (* 4.0 a) c))
275.0ms	(* (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) (/ 1 (* 2.0 a)))
296.0ms	(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

137 → 137

Iterations

Useful iterations: 2 (653.0ms)

Iter	Nodes	Cost
0	242	3748
1	657	3373
2	2553	2889
done	5000	2889

prune480.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.0b

regimes311.0ms

Accuracy

87.8% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 32.0b

bsearch227.0ms

Steps

Iters	Range		Point
8	5.30600492772346e+88	1.193256888551369e+92	9.516392846981132e+91
10	8.134666143579123e-130	4.886277919964174e-120	8.706117685651469e-130
5	-1.9941030622962047e+109	-5.928196142097795e+108	-1.8572382657132166e+109

simplify18.0ms

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	37	71
1	52	69
2	62	67
3	66	67
4	70	67
done	70	67

end0.0ms

sample1.8s

Algorithm

intervals

Results

353.0ms	1069×	body	2560	valid
317.0ms	5791×	body	80	valid
254.0ms	933×	body	1280	valid
149.0ms	2974×	body	80	nan
88.0ms	442×	body	640	valid
47.0ms	122×	body	5120	valid
40.0ms	244×	body	320	valid
14.0ms	126×	body	160	valid