Details

sample39.0ms

Algorithm

intervals

Results

6.0ms	34×	body	2560	valid
6.0ms	180×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	4×	body	320	valid
3.0ms	85×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify61.0ms

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
10.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
50.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify823.0ms

Counts

82 → 82

Iterations

Useful iterations: done (821.0ms)

Iter	Nodes	Cost
0	154	1565
1	395	1463
2	1305	1247
done	5001	1235

prune200.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.4b	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.0b	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

23.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
86.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
58.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
156.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
190.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify907.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (374.0ms)

Iter	Nodes	Cost
0	253	5113
1	618	4541
2	2339	4211
done	5001	4211

prune386.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite79.0ms

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:

17.0ms	(* (* 3.0 a) c)
8.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.4s

Counts

72 → 72

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	120	1001
1	276	903
2	928	825
3	3466	821
done	5000	815

prune171.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ 1 (* 3.0 a))
11.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (* 3.0 a))
52.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (916.0ms)

Iter	Nodes	Cost
0	139	1051
1	331	934
2	1035	830
3	4095	820
done	5001	820

prune172.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.0b

regimes354.0ms

Accuracy

82.4% (5.0b remaining)

Error of 11.1b against oracle of 6.0b and baseline of 34.6b

bsearch95.0ms

Steps

Iters	Range		Point
8	1.7227097696114035e-146	1.4073942755830443e-143	1.3880700472259379e-143
9	-6.105792782810772e+148	-1.3687074167194226e+141	-2.086872071402004e+144

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	32	40
done	32	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

226.0ms	1092×	body	2560	valid
198.0ms	5861×	body	80	valid
146.0ms	917×	body	1280	valid
99.0ms	2943×	body	80	nan
59.0ms	458×	body	640	valid
28.0ms	116×	body	5120	valid
20.0ms	213×	body	320	valid
6.0ms	103×	body	160	valid