Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	195×	body	80	valid
4.0ms	21×	body	1280	valid
4.0ms	3×	body	5120	valid
3.0ms	81×	body	80	nan
3.0ms	19×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

40.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
48.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify915.0ms

Counts

161 → 161

Iterations

Useful iterations: done (896.0ms)

Iter	Nodes	Cost
0	280	4083
1	665	3911
2	1974	3753
done	5001	3752

prune477.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

3251×	`times-frac`
1760×	`add-sqr-sqrt`
1505×	`*-un-lft-identity`
1251×	`add-cube-cbrt`
254×	`difference-of-squares`
130×	`sqrt-prod`
129×	`div-inv`
127×	`distribute-lft-out--`
71×	`associate-/r*`
64×	`add-exp-log`
54×	`div-exp`
25×	`add-cbrt-cube`
15×	`cbrt-undiv` `1-exp` `associate-/r/`
13×	`associate-/l*`
8×	`add-log-exp`
6×	`rec-exp`
5×	`pow1`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 1088

Calls

4 calls:

57.0ms	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
51.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
295.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.6s

Counts

1100 → 1100

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	1483	47686
1	4433	38020
done	5000	37966

prune640.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ 1 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

56.0ms	(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ 1 a))
2.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ 1 a))
51.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify986.0ms

Counts

120 → 120

Iterations

Useful iterations: done (983.0ms)

Iter	Nodes	Cost
0	222	2461
1	623	2249
2	1726	1967
done	5000	1966

prune301.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (314.0ms)

Iter	Nodes	Cost
0	81	1248
1	190	1104
2	599	1036
3	2014	1028
done	5000	1028

prune249.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.5b

regimes202.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch155.0ms

Steps

Iters	Range		Point
10	3.056596725548563e-78	7.076105677608322e-63	3.446447862996811e-75
10	-1.852183237050365e+100	-1.9127319211193897e+86	-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	42
1	35	40
done	35	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

241.0ms	1096×	body	2560	valid
215.0ms	5880×	body	80	valid
157.0ms	852×	body	1280	valid
107.0ms	2945×	body	80	nan
71.0ms	471×	body	640	valid
31.0ms	109×	body	5120	valid
22.0ms	211×	body	320	valid
7.0ms	107×	body	160	valid