Details

sample43.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
8.0ms	195×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	81×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	3×	body	5120	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

prune5.0ms

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))))

rewrite71.0ms

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:

39.0ms	(/ (/ (- (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))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
44.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify861.0ms

Counts

161 → 161

Iterations

Useful iterations: done (855.0ms)

Iter	Nodes	Cost
0	278	4083
1	663	3911
2	1940	3753
done	5000	3752

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize13.0ms

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))))

rewrite199.0ms

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:

52.0ms	(/ (/ 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))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.4s

Counts

1100 → 1100

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	1481	47686
1	4429	38020
done	5001	37966

prune614.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (/ a (/ 1 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))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

348×	`times-frac`
195×	`add-sqr-sqrt`
166×	`*-un-lft-identity`
156×	`add-cube-cbrt`
137×	`associate-r`
56×	`add-exp-log`
28×	`div-exp`
18×	`add-cbrt-cube`
16×	`prod-exp`
13×	`div-inv`
9×	`unswap-sqr`
8×	`rec-exp` `1-exp` `add-log-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`associate-/r/` `cbrt-unprod` `difference-of-squares`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative`

Counts

4 → 229

Calls

4 calls:

118.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (/ a (/ 1 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))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (/ a (/ 1 2.0))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

241 → 241

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	511	5892
1	1386	4536
2	3052	4258
done	5000	4257

prune659.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

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))))

rewrite44.0ms

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))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
80.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (310.0ms)

Iter	Nodes	Cost
0	80	1248
1	189	1104
2	599	1036
3	2025	1028
done	5000	1028

prune242.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes178.0ms

Accuracy

83.3% (4.8b remaining)

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

bsearch136.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	29	42
1	36	42
done	36	42

end0.0ms

sample1.2s

Algorithm

intervals

Results

263.0ms	1096×	body	2560	valid
247.0ms	5880×	body	80	valid
164.0ms	852×	body	1280	valid
112.0ms	2945×	body	80	nan
70.0ms	471×	body	640	valid
33.0ms	109×	body	5120	valid
26.0ms	211×	body	320	valid
8.0ms	107×	body	160	valid