Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
6.0ms	38×	body	1280	valid
6.0ms	177×	body	80	valid
2.0ms	21×	body	640	valid
2.0ms	79×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

35.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	156	1821
1	368	1727
2	997	1611
3	3181	1595
done	5000	1594

prune244.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
4.5b	(/ (/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.7b	(/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

2.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
28.0ms	(/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
148.0ms	(/ (/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
180.0ms	(/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify930.0ms

Counts

196 → 196

Iterations

Useful iterations: done (924.0ms)

Iter	Nodes	Cost
0	302	5540
1	720	4790
2	2596	4614
done	5001	4612

prune470.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
4.5b	(* (/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
9.7b	(/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
52×	`times-frac`
49×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
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 → 138

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(* (/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
27.0ms	(/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
152.0ms	(* (/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
181.0ms	(/ (+ (* a c) 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify884.0ms

Counts

150 → 150

Iterations

Useful iterations: done (880.0ms)

Iter	Nodes	Cost
0	248	3414
1	691	2886
2	2217	2588
done	5000	2586

prune354.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
14.7b	(/ (* a c) a)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ (* a c) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

75 → 75

Iterations

Useful iterations: 3 (830.0ms)

Iter	Nodes	Cost
0	125	880
1	282	798
2	927	698
3	3340	694
done	5001	694

prune166.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.0b

regimes129.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.7b

bsearch141.0ms

Steps

Iters	Range	Point
8	1.5276508475467709e+44	4.1560730947117816e+46	9.965676396086742e+45
8	-3.876848940398081e-247	-7.459891070112096e-252	-7.593271511213179e-252
9	-1.829086240692416e+154	-8.160318760930525e+144	-1.528293454654968e+148

Iters

Range

Point

1.5276508475467709e+44

4.1560730947117816e+46

9.965676396086742e+45

-3.876848940398081e-247

-7.459891070112096e-252

-7.593271511213179e-252

-1.829086240692416e+154

-8.160318760930525e+144

-1.528293454654968e+148

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	59
1	41	59
done	41	59

end0.0ms

sample979.0ms

Algorithm

intervals

Results

213.0ms	1075×	body	2560	valid
185.0ms	5860×	body	80	valid
144.0ms	904×	body	1280	valid
89.0ms	2862×	body	80	nan
55.0ms	457×	body	640	valid
27.0ms	114×	body	5120	valid
19.0ms	211×	body	320	valid
7.0ms	120×	body	160	valid