Details

sample81.0ms

Algorithm

intervals

Results

13.0ms	187×	body	80	valid
12.0ms	29×	body	2560	valid
9.0ms	25×	body	1280	valid
7.0ms	103×	body	80	nan
5.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify149.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite247.0ms

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:

140.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
14.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
64.0ms	(- (* b b) (* (* 4.0 a) c))
135.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: 2 (358.0ms)

Iter	Nodes	Cost
0	154	1592
1	405	1496
2	1789	1332
done	5001	1332

prune423.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
6.2b	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

38.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
84.0ms	(- (* b b) (* (* 4.0 a) c))
170.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

86 → 86

Iterations

Useful iterations: 2 (359.0ms)

Iter	Nodes	Cost
0	163	1718
1	425	1572
2	1722	1436
done	5001	1436

prune567.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(- (* b b) (* (* 4.0 a) c))
9.4b	(- (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ b (* 2.0 a)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

31.0ms	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms	(- (* b b) (* (* 4.0 a) c))
173.0ms	(- (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ b (* 2.0 a)))
29.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(- (* b b) (* (* 4.0 a) c))
197.0ms	(- (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ b (* 2.0 a)))
134.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

133 → 133

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	227	3254
1	615	2918
2	3467	2698
done	5001	2694

prune515.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

localize50.0ms

Local error

Found 4 expressions with local error:

6.2b	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`times-frac` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `distribute-rgt-out--` `diff-log` `frac-sub` `sub-div` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

91.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify611.0ms

Counts

75 → 75

Iterations

Useful iterations: done (608.0ms)

Iter	Nodes	Cost
0	106	1413
1	288	1303
2	1047	1173
done	5000	1171

prune556.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

regimes523.0ms

Accuracy

83.7% (4.7b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.9b

bsearch108.0ms

Steps

Iters	Range		Point
8	3.480389350692124e-86	1.1787098984122044e-83	4.84232518071997e-85
2	-3.2729874464247947e+146	-2.930804953841758e+146	-2.973577765414638e+146

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	50
1	36	50
done	36	50

end0.0ms

sample3.1s

Algorithm

intervals

Results

896.0ms	5854×	body	80	valid
570.0ms	1075×	body	2560	valid
432.0ms	918×	body	1280	valid
232.0ms	2889×	body	80	nan
175.0ms	457×	body	640	valid
151.0ms	110×	body	5120	valid
39.0ms	210×	body	320	valid
14.0ms	108×	body	160	valid