Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
6.0ms	28×	body	2560	valid
6.0ms	31×	body	1280	valid
3.0ms	77×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9
done	105	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize11.0ms

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)))

rewrite106.0ms

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:

64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674
done	5001	674

prune326.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
88.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
221.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify104.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320
done	5001	2320

prune478.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
62.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
131.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
103.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	753	1552
1	3981	1207
2	5001	1195
done	5001	1195

prune251.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.6b	(* (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (/ 1 (* 2.0 a)))
11.7b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

292×	`add-exp-log`
161×	`prod-exp`
108×	`div-exp`
84×	`add-cbrt-cube`
46×	`1-exp`
36×	`cbrt-unprod`
27×	`cbrt-undiv`
18×	`add-sqr-sqrt` `rec-exp`
17×	`*-un-lft-identity`
10×	`pow1` `times-frac`
9×	`add-cube-cbrt`
7×	`associate-r` `associate-/l*`
6×	`add-log-exp`
5×	`sqrt-prod`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `associate-*r/` `pow-prod-down` `flip--`
2×	`distribute-rgt-neg-in` `sqrt-div` `div-inv` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-l` `associate-l/` `clear-num` `associate-/r` `un-div-inv` `*-commutative`

Counts

4 → 159

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
327.0ms	(* (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (/ 1 (* 2.0 a)))
65.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(* (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (/ 1 (* 2.0 a)))
105.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify100.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1037	2482
1	4103	1907
2	5002	1902
done	5002	1902

prune253.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

regimes225.0ms

Accuracy

86.7% (3.6b remaining)

Error of 9.1b against oracle of 5.5b and baseline of 32.7b

bsearch153.0ms

Steps

Iters	Range		Point
8	5.30600492772346e+88	1.193256888551369e+92	6.20818462961119e+88
7	4.4177766368738645e-104	9.228511502033552e-102	4.501804305446481e-104
5	-1.9941030622962047e+109	-5.928196142097795e+108	-1.8572382657132166e+109

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	52	30
2	52	30
done	52	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

254.0ms	1069×	body	2560	valid
234.0ms	5791×	body	80	valid
186.0ms	933×	body	1280	valid
115.0ms	2974×	body	80	nan
69.0ms	442×	body	640	valid
35.0ms	122×	body	5120	valid
27.0ms	244×	body	320	valid
10.0ms	126×	body	160	valid