Details

sample110.0ms

Algorithm

intervals

Results

34.0ms	176×	body	80	valid
24.0ms	42×	body	2560	valid
13.0ms	23×	body	1280	valid
9.0ms	23×	body	640	valid
9.0ms	98×	body	80	nan
3.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize36.0ms

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))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

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--` `insert-posit16` `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 → 95

Calls

4 calls:

48.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* 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)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
47.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	2004
3	2004
2	1046
1	388
0	162

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 191

Calls

4 calls:

40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
112.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
63.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
201.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
289.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

203 → 203

Iterations

Iter	Nodes
done	2000
2	2000
1	736
0	308

prune983.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize84.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (+ 0 (* a c)))
13.1b	(cbrt (+ 0 (* a c)))
13.1b	(cbrt (+ 0 (* a c)))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `sqrt-prod` `flip-+`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt (+ 0 (* a c)))
4.0ms	(cbrt (+ 0 (* a c)))
4.0ms	(cbrt (+ 0 (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (+ 0 (* a c)))
99.0ms	(cbrt (+ 0 (* a c)))
118.0ms	(cbrt (+ 0 (* a c)))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

70 → 70

Iterations

Iter	Nodes
done	2028
4	2028
3	1605
2	514
1	224
0	99

prune472.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.2b

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.4b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
8.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
52×	`times-frac`
51×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `cbrt-unprod` `insert-posit16` `flip--`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
98.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
78.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
203.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
268.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

157 → 157

Iterations

Iter	Nodes
done	2001
2	2001
1	712
0	254

prune740.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.2b

regimes510.0ms

Accuracy

87.2% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 32.5b

bsearch355.0ms

Steps

Iters	Range	Point
7	6.52945691119865e+99	1.3360629297740576e+102	1.4483715500512764e+101
11	1.2714153160963348e-280	4.905829800439075e-261	1.2889142225980239e-280
9	-2.3702445877051193e+75	-7.530140089969592e+69	-1.2810366229709043e+70

Iters

Range

Point

6.52945691119865e+99

1.3360629297740576e+102

1.4483715500512764e+101

1.2714153160963348e-280

4.905829800439075e-261

1.2889142225980239e-280

-2.3702445877051193e+75

-7.530140089969592e+69

-1.2810366229709043e+70

simplify6.0ms

Iterations

Iter	Nodes
done	42
1	42
0	35

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.1s	2935×	body	80	nan
924.0ms	1081×	body	2560	valid
800.0ms	5863×	body	80	valid
728.0ms	902×	body	1280	valid
291.0ms	471×	body	640	valid
115.0ms	218×	body	320	valid
94.0ms	109×	body	5120	valid
27.0ms	115×	body	160	valid