Details

sample410.0ms

Algorithm

intervals

Results

23.0ms	184×	body	80	valid
21.0ms	34×	body	2560	valid
10.0ms	22×	body	1280	valid
9.0ms	89×	body	80	nan
7.0ms	9×	body	5120	valid
5.0ms	14×	body	640	valid
3.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	86
4	86
3	79
2	60
1	38
0	10

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize55.0ms

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))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

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:

46.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
3	3255
2	1440
1	672
0	162

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b	(- (* b_2 b_2) (* a c))
7.2b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`times-frac`
24×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `insert-posit16` `flip--`
3×	`associate-/r*` `distribute-rgt-neg-in` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `div-exp` `frac-sub` `sub-div`

Counts

4 → 101

Calls

4 calls:

16.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
61.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

113 → 113

Iterations

Iter	Nodes
3	3098
2	1468
1	742
0	182

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
10.7b	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

30.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
7.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
41.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

111 → 111

Iterations

Iter	Nodes
3	4277
2	1839
1	879
0	204

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
14.1b	(- (/ (- b_2) a) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
59×	`times-frac`
48×	`sqrt-prod`
26×	`difference-of-squares`
16×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `div-sub` `frac-sub`

Counts

4 → 89

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(- (/ (- b_2) a) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
477.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
132.0ms	(- (/ (- b_2) a) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify854.0ms

Counts

101 → 101

Iterations

Iter	Nodes
3	2893
2	1169
1	554
0	129

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes418.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.5b against oracle of 5.2b and baseline of 33.2b

bsearch125.0ms

Steps

Iters	Range		Point
7	9.852932830556067e+81	3.906369945261731e+83	2.3362227636224895e+83
7	-3.713212020214074e-54	-1.299476807453083e-55	-1.376414644198452e-55

simplify5.0ms

Iterations

Iter	Nodes
2	31
1	31
0	26

end0.0ms

sample3.8s

Algorithm

intervals

Results

949.0ms	898×	body	1280	valid
890.0ms	1057×	body	2560	valid
773.0ms	5867×	body	80	valid
482.0ms	2902×	body	80	nan
191.0ms	440×	body	640	valid
96.0ms	88×	body	5120	valid
84.0ms	252×	body	320	valid
23.0ms	109×	body	160	valid