Details

sample337.0ms

Algorithm

intervals

Results

6.0ms	173×	body	80	valid
6.0ms	29×	body	2560	valid
4.0ms	27×	body	1280	valid
4.0ms	83×	body	80	nan
3.0ms	21×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7
done	29	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.8b	(- (* b_2 b_2) (* a c))
2.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

68.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify39.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705
done	5001	705

prune242.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
54.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
148.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
181.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Counts

212 → 212

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	729	3368
1	3320	3193
2	5001	3167
done	5001	3167

prune503.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b_2 b_2) (* a c))
3.7b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
13.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
58×	`times-frac`
35×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`associate-l`
18×	`add-cbrt-cube`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
6×	`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 → 145

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
56.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
153.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
178.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	700	1931
1	3325	1713
2	5001	1695
done	5001	1695

prune372.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.8b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 485

Calls

4 calls:

45.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
8.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
36.0ms	(- (* b_2 b_2) (* a c))
164.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify92.0ms

Counts

497 → 497

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1536	8629
1	5001	7982
done	5001	7982

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes265.0ms

Accuracy

90% (2.6b remaining)

Error of 8.1b against oracle of 5.5b and baseline of 31.7b

bsearch112.0ms

Steps

Iters	Range	Point
4	9.113314976006761e+77	1.3987841324983815e+78	9.191824015256067e+77
10	8.282891733345819e-215	1.0619437809513192e-203	8.366472411559289e-215
8	-3.942677352963429e+147	-2.908826449852181e+144	-1.3882094406717058e+145

Iters

Range

Point

9.113314976006761e+77

1.3987841324983815e+78

9.191824015256067e+77

8.282891733345819e-215

1.0619437809513192e-203

8.366472411559289e-215

-3.942677352963429e+147

-2.908826449852181e+144

-1.3882094406717058e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	23
1	37	23
done	37	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

213.0ms	1149×	body	2560	valid
197.0ms	5797×	body	80	valid
141.0ms	887×	body	1280	valid
86.0ms	2850×	body	80	nan
61.0ms	474×	body	640	valid
26.0ms	255×	body	320	valid
24.0ms	92×	body	5120	valid
7.0ms	110×	body	160	valid