Details

sample331.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
5.0ms	28×	body	2560	valid
5.0ms	31×	body	1280	valid
2.0ms	77×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 33.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.7b	(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:

70.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

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

prune228.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.2b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

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))
82.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
143.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
174.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Counts

212 → 212

Iterations

Useful iterations: 2 (83.0ms)

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

prune478.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.7b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.6b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
11.2b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(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))
105.0ms	(* (/ (+ 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)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
150.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
176.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (91.0ms)

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

prune362.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.3b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.6b	(* (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) (/ 1 a))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

869×	`times-frac`
572×	`add-sqr-sqrt`
511×	`*-un-lft-identity`
339×	`add-cube-cbrt`
242×	`associate-l`
147×	`add-exp-log`
83×	`div-exp`
78×	`distribute-lft-out--` `difference-of-squares`
42×	`sqrt-prod`
41×	`add-cbrt-cube`
40×	`prod-exp`
39×	`distribute-rgt-neg-in`
25×	`associate-/l*`
22×	`rec-exp` `1-exp`
21×	`unswap-sqr`
19×	`cbrt-undiv` `div-inv`
13×	`associate-r`
9×	`pow1`
8×	`cbrt-unprod`
6×	`add-log-exp`
3×	`pow-prod-down` `associate-/r*`
2×	`flip3--` `pow-flip` `sqrt-div` `div-sub` `flip--` `inv-pow`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l/` `clear-num` `associate-/r/` `un-div-inv` `*-commutative` `associate-/l/`

Counts

4 → 485

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
217.0ms	(* (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) (/ 1 a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
115.0ms	(* (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) (/ 1 a))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Counts

497 → 497

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2185	6931
1	5001	6467
done	5001	6467

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.7b

regimes278.0ms

Accuracy

87.4% (3.4b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 32.6b

bsearch139.0ms

Steps

Iters	Range		Point
8	5.30600492772346e+88	1.193256888551369e+92	9.549485962776621e+89
10	8.134666143579123e-130	4.886277919964174e-120	7.666823646884852e-125
8	-5.7211821970331905e+156	-1.4082798590396656e+153	-8.889080831912834e+153

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	45	25
2	45	25
done	45	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

194.0ms	1071×	body	2560	valid
190.0ms	5788×	body	80	valid
135.0ms	931×	body	1280	valid
91.0ms	2970×	body	80	nan
53.0ms	446×	body	640	valid
27.0ms	122×	body	5120	valid
21.0ms	240×	body	320	valid
7.0ms	130×	body	160	valid