Details

sample125.0ms

Algorithm

intervals

Results

17.0ms	31×	body	2560	valid
17.0ms	184×	body	80	valid
15.0ms	33×	body	1280	valid
8.0ms	90×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify136.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

162.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
17.0ms	(- (* b b) (* (* 4.0 a) c))
93.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
86.0ms	(- (* b b) (* (* 4.0 a) c))
141.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
138.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

84 → 84

Iterations

Useful iterations: 2 (390.0ms)

Iter	Nodes	Cost
0	154	1592
1	405	1496
2	1789	1332
done	5001	1332

prune692.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`prod-exp`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `associate-r`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

295.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
16.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
93.0ms	(- (* b b) (* (* 4.0 a) c))
144.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

93 → 93

Iterations

Useful iterations: 2 (520.0ms)

Iter	Nodes	Cost
0	180	1851
1	485	1693
2	2544	1445
done	5000	1445

prune687.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
5.7b	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

43.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
15.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
96.0ms	(- (* b b) (* (* 4.0 a) c))
202.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: 2 (381.0ms)

Iter	Nodes	Cost
0	163	1718
1	425	1572
2	1722	1436
done	5001	1436

prune650.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt 1) (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(- (* b b) (* (* 4.0 a) c))
9.7b	(- (/ (sqrt 1) (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ b (* 2.0 a)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
65×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
52×	`add-cube-cbrt`
16×	`sqrt-div`
15×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
10×	`flip3--` `flip--`
8×	`div-inv` `add-log-exp`
6×	`associate-/l*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`difference-of-squares`
2×	`sub-neg` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `frac-sub` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

52.0ms	(/ (sqrt 1) (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms	(- (* b b) (* (* 4.0 a) c))
274.0ms	(- (/ (sqrt 1) (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ b (* 2.0 a)))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (sqrt 1) (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c)))))
86.0ms	(- (* b b) (* (* 4.0 a) c))
204.0ms	(- (/ (sqrt 1) (/ (* 2.0 a) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ b (* 2.0 a)))
135.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

164 → 164

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	260	4706
1	674	4020
2	2753	3769
done	5001	3745

prune745.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.7b

regimes503.0ms

Accuracy

82.7% (5.1b remaining)

Error of 10.5b against oracle of 5.4b and baseline of 34.6b

bsearch290.0ms

Steps

Iters	Range		Point
8	7.520261887413394e-140	8.544177483477188e-136	2.4581158795060287e-136
10	-6.623625638726693e+82	-6.4709084601913214e+72	-2.8920328608199634e+82

simplify36.0ms

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	33	53
1	41	52
done	41	52

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1065×	body	2560	valid
1.2s	5800×	body	80	valid
499.0ms	2982×	body	80	nan
437.0ms	908×	body	1280	valid
166.0ms	452×	body	640	valid
160.0ms	122×	body	5120	valid
74.0ms	133×	body	160	valid
64.0ms	231×	body	320	valid