Details

sample66.0ms

Algorithm

intervals

Results

10.0ms	185×	body	80	valid
10.0ms	32×	body	2560	valid
9.0ms	31×	body	1280	valid
6.0ms	108×	body	80	nan
3.0ms	6×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

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:

107.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
50.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
116.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify963.0ms

Counts

103 → 103

Iterations

Useful iterations: done (957.0ms)

Iter	Nodes	Cost
0	156	1821
1	387	1727
2	1508	1613
done	5001	1603

prune368.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`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 → 187

Calls

4 calls:

84.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
128.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
122.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series805.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
272.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
293.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

199 → 199

Iterations

Useful iterations: 2 (785.0ms)

Iter	Nodes	Cost
0	304	5659
1	765	4902
2	4126	4722
done	5001	4722

prune806.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
7.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
52×	`times-frac`
51×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
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 → 141

Calls

4 calls:

61.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
204.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
86.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
271.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
306.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts

153 → 153

Iterations

Useful iterations: 2 (812.0ms)

Iter	Nodes	Cost
0	250	3533
1	730	3010
2	4605	2710
done	5000	2710

prune517.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.8b	(/ (* a c) a)
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

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:

8.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(/ (* a c) a)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(/ (* a c) a)
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

75 → 75

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	125	880
1	313	806
2	1698	726
done	5002	698

prune264.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.8b

regimes226.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.2b against oracle of 5.2b and baseline of 29.3b

bsearch200.0ms

Steps

Iters	Range	Point
6	1.9101351599902807e+102	2.525038855038462e+103	5.550864523265887e+102
8	1.0408663060912465e-291	3.4349488111407062e-289	2.7156356358044857e-290
9	-2.501158360438979e+160	-5.198860796817705e+153	-1.3152753346874725e+154

Iters

Range

Point

1.9101351599902807e+102

2.525038855038462e+103

5.550864523265887e+102

1.0408663060912465e-291

3.4349488111407062e-289

2.7156356358044857e-290

-2.501158360438979e+160

-5.198860796817705e+153

-1.3152753346874725e+154

simplify8.0ms

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	31	53
1	37	51
2	39	49
done	39	49

end0.0ms

sample3.0s

Algorithm

intervals

Results

913.0ms	5806×	body	80	valid
593.0ms	1053×	body	2560	valid
424.0ms	935×	body	1280	valid
204.0ms	2894×	body	80	nan
114.0ms	466×	body	640	valid
86.0ms	233×	body	320	valid
58.0ms	111×	body	5120	valid
12.0ms	106×	body	160	valid