Details

sample192.0ms

Algorithm

intervals

Results

42.0ms	32×	body	2560	valid
40.0ms	171×	body	80	valid
24.0ms	34×	body	1280	valid
13.0ms	13×	body	640	valid
10.0ms	105×	body	80	nan
6.0ms	10×	body	160	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid

simplify460.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	138
7	138
6	136
5	131
4	126
3	107
2	61
1	28
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

246.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
25.0ms	(- (* b b) (* 4.0 (* a c)))
151.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
39.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series968.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
140.0ms	(- (* b b) (* 4.0 (* a c)))
233.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
293.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify16.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4826
2	1269
1	409
0	157

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* c (* 4.0 a))))) (* 2.0 a))
1.0b	(- (* b b) (* c (* 4.0 a)))
2.4b	(- (- b) (sqrt (- (* b b) (* c (* 4.0 a)))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

279.0ms	(/ (- (- b) (sqrt (- (* b b) (* c (* 4.0 a))))) (* 2.0 a))
21.0ms	(- (* b b) (* c (* 4.0 a)))
68.0ms	(- (- b) (sqrt (- (* b b) (* c (* 4.0 a)))))
29.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series1.4s

Counts

4 → 12

Calls

4 calls:

540.0ms	(/ (- (- b) (sqrt (- (* b b) (* c (* 4.0 a))))) (* 2.0 a))
240.0ms	(- (* b b) (* c (* 4.0 a)))
336.0ms	(- (- b) (sqrt (- (* b b) (* c (* 4.0 a)))))
320.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify8.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1311
1	414
0	159

prune2.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize418.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite908.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

545.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
126.0ms	(- (* b b) (* 4.0 (* a c)))
109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.5s

Counts

4 → 12

Calls

4 calls:

524.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
248.0ms	(- (* b b) (* 4.0 (* a c)))
378.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
341.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify5.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1679
1	474
0	183

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.1b

regimes916.0ms

Accuracy

85.4% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 34.2b

bsearch332.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	6.0605931798902975e+143
8	-1.9399997713196595e-50	-4.155540846280759e-54	-9.446364120144488e-54

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample16.5s

Algorithm

intervals

Results

4.3s	1056×	body	2560	valid
3.1s	230×	body	320	valid
2.5s	449×	body	640	valid
2.0s	103×	body	5120	valid
1.7s	5836×	body	80	valid
1.3s	909×	body	1280	valid
727.0ms	2825×	body	80	nan
46.0ms	127×	body	160	valid