Details

sample170.0ms

Algorithm

intervals

Results

16.0ms	32×	body	2560	valid
14.0ms	176×	body	80	valid
11.0ms	29×	body	1280	valid
8.0ms	85×	body	80	nan
5.0ms	16×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	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: 34.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

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:

62.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
45.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
3	2584
2	1011
1	386
0	162

prune539.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite216.0ms

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:

43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
105.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
45.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
229.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
258.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify980.0ms

Counts

203 → 203

Iterations

Iter	Nodes
2	2212
1	728
0	308

prune826.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.1b	(/ (* a c) a)
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-/r*` `times-frac` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 67

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(/ (* a c) a)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(/ (* a c) a)
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

79 → 79

Iterations

Iter	Nodes
3	3328
2	886
1	299
0	129

prune368.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.2b	(/ a (* a c))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod` `insert-posit16`
3×	`times-frac` `flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--`

Counts

4 → 67

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(/ a (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(/ a (* a c))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
3	2614
2	815
1	282
0	129

prune315.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes405.0ms

Accuracy

88.3% (3.0b remaining)

Error of 8.5b against oracle of 5.6b and baseline of 30.8b

bsearch225.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
7	-1.346954522507992e-154	-2.260619354048848e-156	-9.19692552328612e-155
2	-8.519118707171572e+64	-7.217464048007885e+64	-8.03099820998519e+64

simplify6.0ms

Iterations

Iter	Nodes
2	40
1	40
0	34

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	5788×	body	80	valid
824.0ms	1053×	body	2560	valid
529.0ms	956×	body	1280	valid
377.0ms	2937×	body	80	nan
229.0ms	453×	body	640	valid
138.0ms	216×	body	320	valid
101.0ms	98×	body	5120	valid
57.0ms	108×	body	160	valid