Details

sample325.0ms

Algorithm

intervals

Results

16.0ms	29×	body	2560	valid
15.0ms	202×	body	80	valid
11.0ms	31×	body	1280	valid
7.0ms	106×	body	80	nan
3.0ms	9×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

430.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
45.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify882.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1459
1	384
0	154

prune567.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

203.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
6.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
64.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.8s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2888
1	454
0	174

prune473.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b	(sqrt (- (* b_2 b_2) (* a c)))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

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×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

35.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
58.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series816.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
129.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))
474.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3680
2	717
1	191
0	78

prune506.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.9b

localize12.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.9b

regimes593.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 34.5b

bsearch116.0ms

Steps

Iters	Range		Point
8	1.5119020269574885e-23	1.8921341643334238e-20	9.136492990928292e-23
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample2.7s

Algorithm

intervals

Results

516.0ms	1059×	body	2560	valid
500.0ms	115×	body	160	valid
496.0ms	5860×	body	80	valid
345.0ms	902×	body	1280	valid
247.0ms	2871×	body	80	nan
128.0ms	434×	body	640	valid
54.0ms	124×	body	5120	valid
36.0ms	224×	body	320	valid