Details

sample51.0ms

Algorithm

intervals

Results

9.0ms	35×	body	2560	valid
8.0ms	185×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	103×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	7×	body	160	valid
1.0ms	4×	body	320	valid

simplify59.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite165.0ms

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:

99.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
47.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify842.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1527
1	392
0	158

prune501.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite121.0ms

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:

73.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
6.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
52.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	3515
1	665
0	266

prune603.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b	(- (* b_2 b_2) (* a c))
5.6b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

23.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
9.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
42.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify872.0ms

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1491
1	418
0	178

prune645.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
12.5b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (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)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify605.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1037
1	252
0	96

prune528.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

regimes570.0ms

Accuracy

87.8% (3.6b remaining)

Error of 9.0b against oracle of 5.4b and baseline of 34.7b

bsearch160.0ms

Steps

Iters	Range	Point
9	6.258218916731328e+93	1.8883840965187804e+99	6.382246919184672e+97
7	-1.9525004674970017e-146	-8.640740768077714e-148	-4.749476137934257e-147
7	-1.2092396089946692e+59	-6.172175216823688e+56	-2.5812914736950297e+58

Iters

Range

Point

6.258218916731328e+93

1.8883840965187804e+99

6.382246919184672e+97

-1.9525004674970017e-146

-8.640740768077714e-148

-4.749476137934257e-147

-1.2092396089946692e+59

-6.172175216823688e+56

-2.5812914736950297e+58

simplify4.0ms

Iterations

Iter	Nodes
done	48
1	48
0	37

end0.0ms

sample3.0s

Algorithm

intervals

Results

893.0ms	5778×	body	80	valid
563.0ms	1115×	body	2560	valid
449.0ms	885×	body	1280	valid
260.0ms	2929×	body	80	nan
121.0ms	463×	body	640	valid
103.0ms	254×	body	320	valid
53.0ms	111×	body	5120	valid
15.0ms	124×	body	160	valid