Details

sample86.0ms

Algorithm

intervals

Results

20.0ms	42×	body	2560	valid
14.0ms	173×	body	80	valid
10.0ms	25×	body	1280	valid
6.0ms	18×	body	640	valid
5.0ms	69×	body	80	nan
3.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize11.0ms

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))))
1.2b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

127.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
113.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

103 → 103

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	156	1821
1	366	1727
2	1005	1611
3	2770	1595
done	5001	1593

prune329.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.4b	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.8b	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
62.0ms	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b_2 b_2) (* a c))
269.0ms	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
321.0ms	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

136 → 136

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	237	2999
1	586	2794
2	1938	2466
done	5001	2460

prune541.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

74.0ms	(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
127.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

169 → 169

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	262	3935
1	591	3277
2	1139	3153
3	2516	3149
done	5000	3137

prune356.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

67.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
58.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
121.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

189 → 189

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	266	4484
1	577	3936
2	1380	3617
3	3854	3507
done	5000	3507

prune453.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

regimes309.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.6b

bsearch264.0ms

Steps

Iters	Range	Point
5	1.7897742140858872e+53	5.1194650287633095e+53	5.031608061939103e+53
9	9.448397398655464e-278	1.4829972419072586e-270	8.216265756828381e-276
9	-1.4642911230069481e+159	-8.435593739772907e+149	-3.5132588248780117e+152

Iters

Range

Point

1.7897742140858872e+53

5.1194650287633095e+53

5.031608061939103e+53

9.448397398655464e-278

1.4829972419072586e-270

8.216265756828381e-276

-1.4642911230069481e+159

-8.435593739772907e+149

-3.5132588248780117e+152

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	33	57
1	39	55
done	39	55

end0.0ms

sample3.1s

Algorithm

intervals

Results

967.0ms	5843×	body	80	valid
500.0ms	1104×	body	2560	valid
458.0ms	860×	body	1280	valid
267.0ms	2938×	body	80	nan
120.0ms	492×	body	640	valid
112.0ms	106×	body	160	valid
51.0ms	107×	body	5120	valid
41.0ms	226×	body	320	valid