Details

sample85.0ms

Algorithm

intervals

Results

15.0ms	32×	body	2560	valid
14.0ms	184×	body	80	valid
11.0ms	30×	body	1280	valid
7.0ms	24×	body	640	valid
6.0ms	83×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify179.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite135.0ms

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:

85.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
71.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
84.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	157	1750
1	402	1650
2	1317	1474
3	4966	1459
done	5000	1459

prune448.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
2.5b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.1b	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
20×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`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 → 138

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
176.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
88.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series701.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* b b) (* 4.0 (* a c)))
251.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
286.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
91.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

150 → 150

Iterations

Useful iterations: 2 (644.0ms)

Iter	Nodes	Cost
0	252	4460
1	615	3954
2	2461	3652
done	5001	3652

prune711.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
2.6b	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.1b	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

18.0ms	(- (* b b) (* 4.0 (* a c)))
193.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
117.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series780.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* 4.0 (* a c)))
308.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
306.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

148 → 148

Iterations

Useful iterations: 2 (657.0ms)

Iter	Nodes	Cost
0	257	4174
1	674	3610
2	2709	3178
done	5000	3178

prune649.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b	(- (* b b) (* 4.0 (* a c)))
11.9b	(/ (* (* 4.0 a) c) (* 2.0 a))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

70.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(/ (* (* 4.0 a) c) (* 2.0 a))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
65.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(/ (* (* 4.0 a) c) (* 2.0 a))
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

79 → 79

Iterations

Useful iterations: 2 (390.0ms)

Iter	Nodes	Cost
0	150	1246
1	393	1128
2	1995	964
done	5001	964

prune200.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

regimes203.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.7b

bsearch184.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.7151811081882383e+78
9	3.6976431258031608e-267	1.8292500652683027e-260	7.061692521831336e-266
8	-6.990724105819741e+111	-2.6156774686163576e+108	-5.674469085146397e+110

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.7151811081882383e+78

3.6976431258031608e-267

1.8292500652683027e-260

7.061692521831336e-266

-6.990724105819741e+111

-2.6156774686163576e+108

-5.674469085146397e+110

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	57
1	38	57
done	38	57

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	5913×	body	80	valid
487.0ms	1081×	body	2560	valid
376.0ms	891×	body	1280	valid
232.0ms	3009×	body	80	nan
159.0ms	468×	body	640	valid
79.0ms	216×	body	320	valid
53.0ms	107×	body	5120	valid
14.0ms	100×	body	160	valid