Details

sample82.0ms

Algorithm

intervals

Results

15.0ms	197×	body	80	valid
13.0ms	28×	body	2560	valid
11.0ms	31×	body	1280	valid
5.0ms	77×	body	80	nan
3.0ms	11×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify119.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite159.0ms

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:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(- (* b b) (* (* 4.0 a) c))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	154	1565
1	401	1461
2	1342	1245
done	5001	1233

prune408.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.8b	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.4b	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
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 → 148

Calls

4 calls:

14.0ms	(- (* b b) (* (* 4.0 a) c))
123.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
72.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series645.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* b b) (* (* 4.0 a) c))
234.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
240.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

160 → 160

Iterations

Useful iterations: 2 (727.0ms)

Iter	Nodes	Cost
0	252	4912
1	623	4364
2	2681	4036
done	5000	4036

prune617.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.8b	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
11.7b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
122×	`add-exp-log`
76×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
63×	`div-exp`
58×	`add-cbrt-cube`
45×	`associate-/l*`
43×	`add-cube-cbrt`
34×	`prod-exp`
27×	`cbrt-undiv`
16×	`distribute-lft-out--` `difference-of-squares`
14×	`cbrt-unprod`
11×	`sqrt-prod`
10×	`div-inv`
8×	`rec-exp` `distribute-rgt-neg-in` `1-exp`
6×	`add-log-exp`
5×	`pow1`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 185

Calls

4 calls:

16.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
127.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4.0 a) c))
176.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
162.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

197 → 197

Iterations

Useful iterations: 2 (686.0ms)

Iter	Nodes	Cost
0	384	5941
1	987	5560
2	3339	4669
done	5000	4669

prune529.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
14.7b	(/ (* 4.0 (* a c)) a)
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(/ (* 4.0 (* a c)) a)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (* 4.0 (* a c)) a)
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

80 → 80

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	150	1194
1	371	1095
2	1452	917
done	5000	907

prune358.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.0b

regimes307.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.7b

bsearch154.0ms

Steps

Iters	Range	Point
8	1.4961070689597945e+139	4.5158951869773294e+141	1.292564275165585e+140
7	4.538743239886903e-308	1.8932238735467414e-306	4.631041364691663e-308
5	-1.9941030622962047e+109	-5.928196142097795e+108	-1.8572382657132166e+109

Iters

Range

Point

1.4961070689597945e+139

4.5158951869773294e+141

1.292564275165585e+140

4.538743239886903e-308

1.8932238735467414e-306

4.631041364691663e-308

-1.9941030622962047e+109

-5.928196142097795e+108

-1.8572382657132166e+109

simplify5.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	38	66
1	46	65
done	46	65

end0.0ms

sample1.9s

Algorithm

intervals

Results

364.0ms	1069×	body	2560	valid
331.0ms	5791×	body	80	valid
256.0ms	933×	body	1280	valid
160.0ms	2974×	body	80	nan
101.0ms	442×	body	640	valid
52.0ms	122×	body	5120	valid
39.0ms	244×	body	320	valid
14.0ms	126×	body	160	valid