Details

sample156.0ms

Algorithm

intervals

Results

15.0ms	44×	body	2560	valid
11.0ms	167×	body	80	valid
9.0ms	32×	body	1280	valid
7.0ms	100×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite167.0ms

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:

78.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
59.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
359.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	151	1534
1	377	1440
2	1547	1268
done	5000	1260

prune369.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.3b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite244.0ms

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:

11.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
83.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b_2 b_2) (* a c))
229.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
243.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

212 → 212

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	301	6227
1	775	5392
2	4300	5196
done	5000	5192

prune833.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize19.0ms

Local error

Found 4 expressions with local error:

8.4b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
10.4b	(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`flip3--` `sqrt-div` `associate-/r*` `flip--`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 80

Calls

4 calls:

13.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
37.0ms	(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
273.0ms	(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

92 → 92

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	157	2560
1	405	1585
2	2075	1477
done	5000	1455

prune636.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.4b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
11.3b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite308.0ms

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:

9.0ms	(- (* b_2 b_2) (* a c))
170.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
103.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b_2 b_2) (* a c))
219.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
291.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts

157 → 157

Iterations

Useful iterations: 2 (997.0ms)

Iter	Nodes	Cost
0	247	3706
1	739	3169
2	4978	2833
done	5002	2833

prune558.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

regimes376.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.2b

bsearch246.0ms

Steps

Iters	Range		Point
7	517946.10598021303	17102963.46615162	811154.206078971
11	6.169740529460457e-151	4.897960687835475e-129	1.8822806382193986e-149
8	-1.471055469501053e+100	-2.16094220789435e+96	-1.8069356592732734e+98

simplify14.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	34	61
1	41	59
2	42	59
done	42	59

end0.0ms

sample3.4s

Algorithm

intervals

Results

757.0ms	2902×	body	80	nan
530.0ms	5719×	body	80	valid
499.0ms	224×	body	320	valid
461.0ms	1131×	body	2560	valid
436.0ms	936×	body	1280	valid
135.0ms	446×	body	640	valid
57.0ms	111×	body	5120	valid
13.0ms	110×	body	160	valid