Details

sample270.0ms

Algorithm

intervals

Results

56.0ms	89×	body	80	nan
32.0ms	39×	body	2560	valid
30.0ms	187×	body	80	valid
19.0ms	28×	body	1280	valid
5.0ms	10×	body	640	valid
4.0ms	9×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	3×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	29
5	29
4	27
3	25
2	22
1	14
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite282.0ms

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--` `insert-posit16` `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 → 88

Calls

4 calls:

113.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (* b_2 b_2) (* a c))
125.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
44.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
206.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
3	2917
2	997
1	376
0	158

prune932.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

128.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
7.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
46.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.0s

Counts

101 → 101

Iterations

Iter	Nodes
3	4222
2	1338
1	442
0	178

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

136.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

104 → 104

Iterations

Iter	Nodes
3	3139
2	1139
1	428
0	166

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite153.0ms

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` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

76 → 76

Iterations

Iter	Nodes
4	3591
3	1497
2	533
1	183
0	80

prune896.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

regimes360.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.6b

bsearch184.0ms

Steps

Iters	Range		Point
8	6.256891986679925e-86	3.543466061308676e-83	4.6659701943749105e-84
8	-6.435448379097954e+123	-1.4863434806956936e+121	-3.279807108380076e+121

simplify4.0ms

Iterations

Iter	Nodes
2	31
1	31
0	26

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	5846×	body	80	valid
945.0ms	1107×	body	2560	valid
687.0ms	934×	body	1280	valid
334.0ms	2915×	body	80	nan
227.0ms	454×	body	640	valid
94.0ms	113×	body	5120	valid
71.0ms	210×	body	320	valid
48.0ms	112×	body	160	valid