Details

sample68.0ms

Algorithm

intervals

Results

14.0ms	37×	body	2560	valid
13.0ms	198×	body	80	valid
6.0ms	107×	body	80	nan
6.0ms	19×	body	1280	valid
3.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

89.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
3	3608
2	1039
1	383
0	158

prune609.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

85.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
12.0ms	(- (* b_2 b_2) (* a c))
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
55.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
3	4344
2	1310
1	450
0	177

prune580.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite140.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

71.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
49.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.4s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
3	3608
2	1039
1	383
0	158

prune497.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite144.0ms

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×	`add-cbrt-cube` `associate-/r/`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 177

Calls

4 calls:

80.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
45.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

189 → 189

Iterations

Iter	Nodes
done	5002
2	1752
1	650
0	266

prune739.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

regimes456.0ms

Accuracy

83.6% (4.6b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.8b

bsearch121.0ms

Steps

Iters	Range		Point
6	4.2942163002471454e+116	2.920461936675284e+117	2.865381670376961e+117
9	-2.9209995635511727e-62	-5.172501488366762e-68	-2.5694949190681246e-64

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	22

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	1038×	body	2560	valid
459.0ms	5910×	body	80	valid
451.0ms	909×	body	1280	valid
276.0ms	2910×	body	80	nan
117.0ms	444×	body	640	valid
90.0ms	110×	body	5120	valid
46.0ms	238×	body	320	valid
14.0ms	108×	body	160	valid