Details

sample235.0ms

Algorithm

intervals

Results

84.0ms	198×	body	80	valid
28.0ms	31×	body	2560	valid
20.0ms	28×	body	1280	valid
13.0ms	87×	body	80	nan
10.0ms	18×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize488.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite131.0ms

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:

72.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5004
3	3752
2	1082
1	388
0	162

prune575.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.1b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
59.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series669.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
210.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
264.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	2195
1	614
0	241

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.4b	(- (* b_2 b_2) (* a c))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 158

Calls

4 calls:

57.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
14.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
46.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

170 → 170

Iterations

Iter	Nodes
done	5002
2	1969
1	653
0	259

prune540.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)
0.4b	(- (* b_2 b_2) (* a c))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`associate-l`
20×	`times-frac`
16×	`add-cube-cbrt`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`flip3--` `prod-exp` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`associate-r` `unswap-sqr`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/` `cbrt-unprod`
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:

151.0ms	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)
8.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)
46.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5007
3	3960
2	1311
1	426
0	175

prune394.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.5b

regimes566.0ms

Accuracy

95% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.5b

bsearch231.0ms

Steps

Iters	Range	Point
9	6.2301214455520334e+75	1.9082112581546424e+85	3.4243727332802643e+80
10	-7.515465345640067e-297	7.460393016724008e-306	-1.092790018801933e-307
6	-4.186518194588193e+147	-8.063856753082807e+146	-1.1942109607748042e+147

Iters

Range

Point

6.2301214455520334e+75

1.9082112581546424e+85

3.4243727332802643e+80

-7.515465345640067e-297

7.460393016724008e-306

-1.092790018801933e-307

-4.186518194588193e+147

-8.063856753082807e+146

-1.1942109607748042e+147

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.3s	5839×	body	80	valid
798.0ms	1060×	body	2560	valid
556.0ms	889×	body	1280	valid
489.0ms	2843×	body	80	nan
198.0ms	456×	body	640	valid
92.0ms	114×	body	5120	valid
72.0ms	228×	body	320	valid
26.0ms	121×	body	160	valid