Details

sample60.0ms

Algorithm

intervals

Results

12.0ms	37×	body	2560	valid
9.0ms	182×	body	80	valid
8.0ms	31×	body	1280	valid
5.0ms	22×	body	640	valid
4.0ms	89×	body	80	nan
1.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	5120	valid

simplify42.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 171

Calls

4 calls:

90.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
40.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
116.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	1505
1	573
0	244

prune771.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize97.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	1495
2	455
1	161
0	67

prune647.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize94.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	1495
2	455
1	161
0	67

prune645.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

10.0ms

(* -1/2 (/ c b_2))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(* -1/2 (/ c b_2))

simplify1.8s

Counts

37 → 37

Iterations

Iter	Nodes
done	5002
3	1799
2	519
1	172
0	70

prune138.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 5.2b

regimes636.0ms

Accuracy

84.5% (4.4b remaining)

Error of 10.6b against oracle of 6.2b and baseline of 34.6b

bsearch108.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	2.87562986234827e+107
9	-1.0952546209266604e-55	-7.034794544076098e-65	-9.332433396832084e-58

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	27

end0.0ms

sample2.8s

Algorithm

intervals

Results

949.0ms	1019×	body	2560	valid
571.0ms	5889×	body	80	valid
283.0ms	891×	body	1280	valid
275.0ms	2880×	body	80	nan
236.0ms	461×	body	640	valid
46.0ms	98×	body	5120	valid
42.0ms	223×	body	320	valid
14.0ms	117×	body	160	valid