Details

sample72.0ms

Algorithm

intervals

Results

15.0ms	193×	body	80	valid
14.0ms	30×	body	2560	valid
12.0ms	31×	body	1280	valid
7.0ms	91×	body	80	nan
4.0ms	14×	body	640	valid
3.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	44
4	44
3	41
2	32
1	18
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

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:

52.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
126.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

107 → 107

Iterations

Iter	Nodes
3	2560
2	1015
1	388
0	162

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 93

Calls

4 calls:

80.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
99.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

105 → 105

Iterations

Iter	Nodes
3	4203
2	1280
1	452
0	181

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite121.0ms

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:

52.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
126.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify948.0ms

Counts

107 → 107

Iterations

Iter	Nodes
3	2560
2	1015
1	388
0	162

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.1b

localize51.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.3b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
17.8b	(- (* b_2 b_2) (* b_2 b_2))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`insert-posit16`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`sum-log` `flip3-+` `flip3--` `sqrt-div` `associate-+l-` `flip-+` `flip--` `distribute-lft-out` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `+-inverses` `diff-log` `div-sub` `div-exp` `neg-log` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
16.0ms	(- (* b_2 b_2) (* b_2 b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
3	2665
2	906
1	369
0	158

prune878.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.1b

regimes395.0ms

Accuracy

93.6% (1.5b remaining)

Error of 6.9b against oracle of 5.4b and baseline of 29.4b

bsearch277.0ms

Steps

Iters	Range	Point
9	2.1762368803982262e+45	1.3534154308951418e+51	5.646875521171257e+50
10	-1.42643309478481e-241	-6.497739978200133e-255	-6.590101287064612e-255
8	-1.7996802595953755e+64	-1.2634430355867738e+61	-2.6063173736106266e+63

Iters

Range

Point

2.1762368803982262e+45

1.3534154308951418e+51

5.646875521171257e+50

-1.42643309478481e-241

-6.497739978200133e-255

-6.590101287064612e-255

-1.7996802595953755e+64

-1.2634430355867738e+61

-2.6063173736106266e+63

simplify30.0ms

Iterations

Iter	Nodes
2	35
1	35
0	30

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	1016×	body	2560	valid
686.0ms	5884×	body	80	valid
545.0ms	908×	body	1280	valid
509.0ms	122×	body	5120	valid
289.0ms	2869×	body	80	nan
179.0ms	441×	body	640	valid
72.0ms	239×	body	320	valid
21.0ms	113×	body	160	valid