Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
7.0ms	24×	body	1280	valid
7.0ms	183×	body	80	valid
3.0ms	84×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	63	17
3	114	17
4	130	17
5	136	17
6	139	17
done	139	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

34.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify735.0ms

Counts

89 → 89

Iterations

Useful iterations: done (732.0ms)

Iter	Nodes	Cost
0	157	1750
1	405	1650
2	1328	1474
done	5000	1459

prune240.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

41.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
46.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify736.0ms

Counts

176 → 176

Iterations

Useful iterations: done (729.0ms)

Iter	Nodes	Cost
0	283	4621
1	679	4441
2	2018	4265
done	5001	4264

prune415.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
37×	`times-frac`
26×	`add-exp-log`
25×	`associate-l`
23×	`add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`associate-r`
10×	`add-log-exp`
8×	`div-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp` `div-inv`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 114

Calls

4 calls:

60.0ms	(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify658.0ms

Counts

126 → 126

Iterations

Useful iterations: done (654.0ms)

Iter	Nodes	Cost
0	225	2680
1	635	2466
2	1780	2162
done	5001	2161

prune289.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

3701×	`times-frac`
1907×	`add-sqr-sqrt`
1906×	`*-un-lft-identity`
1398×	`add-cube-cbrt`
254×	`distribute-lft-out--` `difference-of-squares`
138×	`div-inv`
130×	`sqrt-prod`
127×	`distribute-rgt-neg-in`
80×	`associate-/r*`
64×	`add-exp-log`
54×	`div-exp`
25×	`add-cbrt-cube`
15×	`cbrt-undiv` `1-exp` `associate-/r/`
13×	`associate-/l*`
10×	`add-log-exp`
6×	`rec-exp`
5×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 1217

Calls

4 calls:

59.0ms	(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
49.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.9s

Counts

1229 → 1229

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	1489	54153
1	4453	43162
done	5000	43106

prune611.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes190.0ms

Accuracy

82.3% (5.0b remaining)

Error of 10.3b against oracle of 5.3b and baseline of 33.7b

bsearch68.0ms

Steps

Iters	Range		Point
9	1.790439840991813e+53	4.6520850645607246e+61	1.3316184968738608e+61
2	-4.223797038045246e-104	-3.7861133082378615e-104	-4.1690865718193236e-104

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	39
1	34	37
done	34	37

end0.0ms

sample1.1s

Algorithm

intervals

Results

251.0ms	1069×	body	2560	valid
225.0ms	5865×	body	80	valid
151.0ms	828×	body	1280	valid
107.0ms	2882×	body	80	nan
68.0ms	477×	body	640	valid
30.0ms	110×	body	5120	valid
27.0ms	248×	body	320	valid
8.0ms	113×	body	160	valid