Details

sample47.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	175×	body	80	valid
6.0ms	32×	body	1280	valid
4.0ms	104×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	114	17
4	130	17
5	137	17
6	141	17
done	141	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite122.0ms

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:

72.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
85.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	157	1750
1	402	1650
2	1322	1474
3	4955	1459
done	5000	1459

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.9b	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.2b	(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

47.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
111.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
73.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
208.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
207.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

153 → 153

Iterations

Useful iterations: 2 (455.0ms)

Iter	Nodes	Cost
0	253	4579
1	622	4057
2	2571	3753
done	5000	3753

prune446.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.6b	(/ (* 2.0 a) (/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
11.2b	(/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

47.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
75.0ms	(/ (* 2.0 a) (/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
68.0ms	(/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
96.0ms	(/ (* 2.0 a) (/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
210.0ms	(/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

125 → 125

Iterations

Useful iterations: 2 (467.0ms)

Iter	Nodes	Cost
0	226	3312
1	612	3108
2	2927	2426
done	5002	2426

prune335.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* 2.0 (* (/ 1 (* 4.0 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

350.0ms	(/ 1 (* 2.0 (* (/ 1 (* 4.0 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
12.0ms	(- (* b b) (* 4.0 (* a c)))
47.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ 1 (* 2.0 (* (/ 1 (* 4.0 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

112 → 112

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	229	2465
1	551	2113
2	1931	1765
done	5002	1761

prune217.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.4b

regimes247.0ms

Accuracy

76.9% (5.5b remaining)

Error of 10.8b against oracle of 5.3b and baseline of 29.1b

bsearch210.0ms

Steps

Iters	Range		Point
9	1.3160112691565966e-63	6.814126701934224e-57	1.8707090817434317e-63
6	3.6410892437809104e-110	3.0960233903298005e-109	3.7052502960789305e-110
8	1.0691773024250323e-170	5.5548132533506025e-168	5.330769455174493e-168
9	-1.4924982923623064e+60	-5.817343306680769e+54	-3.203999247190538e+59

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	77
1	49	73
done	49	73

end0.0ms

sample1.3s

Algorithm

intervals

Results

254.0ms	1077×	body	2560	valid
232.0ms	5761×	body	80	valid
177.0ms	912×	body	1280	valid
110.0ms	2832×	body	80	nan
71.0ms	463×	body	640	valid
30.0ms	105×	body	5120	valid
28.0ms	249×	body	320	valid
9.0ms	118×	body	160	valid