Details

sample82.0ms

Algorithm

intervals

Results

31.0ms	37×	body	2560	valid
13.0ms	186×	body	80	valid
10.0ms	28×	body	1280	valid
6.0ms	91×	body	80	nan
6.0ms	20×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify21.0ms

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: 34.6b

localize19.0ms

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))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

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:

75.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
57.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

107 → 107

Iterations

Iter	Nodes
3	2584
2	1011
1	386
0	162

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize35.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite232.0ms

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:

63.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
104.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
51.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
195.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
238.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

203 → 203

Iterations

Iter	Nodes
2	2212
1	728
0	308

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.3b	(/ (* a c) a)
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

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:

16.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(/ (* a c) a)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(/ (* a c) a)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
3	3328
2	886
1	299
0	129

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.4b	(* (* a c) (/ 1 a))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`associate-r`
12×	`prod-exp` `add-cube-cbrt`
10×	`pow1`
9×	`times-frac`
8×	`add-log-exp`
6×	`cbrt-unprod`
4×	`div-exp` `sqrt-prod` `insert-posit16`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-r/` `un-div-inv` `-commutative` `div-inv` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(* (* a c) (/ 1 a))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(* (* a c) (/ 1 a))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

96 → 96

Iterations

Iter	Nodes
3	3619
2	1185
1	425
0	163

prune985.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.7b

regimes468.0ms

Accuracy

87.7% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 31.5b

bsearch334.0ms

Steps

Iters	Range	Point
8	6.45623811977989e+97	1.5556153764929518e+101	2.8498539378971727e+99
8	-2.421027641776492e-112	-4.272667157741124e-116	-3.7117535086124408e-115
7	-1.542727211461463e+154	-3.8584650617426363e+152	-4.0756890097990247e+152

Iters

Range

Point

6.45623811977989e+97

1.5556153764929518e+101

2.8498539378971727e+99

-2.421027641776492e-112

-4.272667157741124e-116

-3.7117535086124408e-115

-1.542727211461463e+154

-3.8584650617426363e+152

-4.0756890097990247e+152

simplify11.0ms

Iterations

Iter	Nodes
2	40
1	40
0	34

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.2s	5836×	body	80	valid
969.0ms	1100×	body	2560	valid
625.0ms	918×	body	1280	valid
408.0ms	2972×	body	80	nan
266.0ms	497×	body	640	valid
149.0ms	107×	body	5120	valid
67.0ms	194×	body	320	valid
27.0ms	118×	body	160	valid