Details

sample114.0ms

Algorithm

intervals

Results

26.0ms	186×	body	80	valid
23.0ms	29×	body	2560	valid
17.0ms	24×	body	1280	valid
11.0ms	88×	body	80	nan
9.0ms	17×	body	640	valid
5.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid

simplify118.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.6b	(- (* b b) (* (* c a) 4))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite164.0ms

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:

94.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
53.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(- (* b b) (* (* c a) 4))
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
117.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
70.0ms	(- (* b b) (* (* c a) 4))
91.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
3	3543
2	1090
1	400
0	161

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.6b	(- (* b b) (* (* c a) 4))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `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` `pow-flip` `inv-pow`

Counts

4 → 166

Calls

4 calls:

63.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
40.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
13.0ms	(- (* b b) (* (* c a) 4))
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
102.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
69.0ms	(- (* b b) (* (* c a) 4))
99.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.3s

Counts

178 → 178

Iterations

Iter	Nodes
3	6148
2	1867
1	647
0	265

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize62.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* c a) 4))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

15.0ms	(- (* b b) (* (* c a) 4))
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))
15.0ms	(sqrt (- (* b b) (* (* c a) 4)))
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* c a) 4))
100.0ms	(sqrt (- (* b b) (* (* c a) 4)))
96.0ms	(sqrt (- (* b b) (* (* c a) 4)))
84.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify4.8s

Counts

73 → 73

Iterations

Iter	Nodes
4	7516
3	1825
2	493
1	161
0	63

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize83.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (- (* b b) (* (* c a) 4)))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))
24.4b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `flip--` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* c a) 4)))
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))
15.0ms	(sqrt (- (* b b) (* (* c a) 4)))
25.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (- (* b b) (* (* c a) 4)))
113.0ms	(sqrt (- (* b b) (* (* c a) 4)))
121.0ms	(sqrt (- (* b b) (* (* c a) 4)))
87.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.9s

Counts

76 → 76

Iterations

Iter	Nodes
4	5174
3	1403
2	414
1	130
0	52

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes727.0ms

Accuracy

84.3% (4.4b remaining)

Error of 10.3b against oracle of 5.9b and baseline of 34.0b

bsearch207.0ms

Steps

Iters	Range		Point
9	2.5177836961106285e-119	1.1213560046341023e-113	7.296044290893796e-114
7	-4.611849920572465e+95	-3.3021145473587595e+93	-3.177289780863109e+94

simplify10.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.1s	912×	body	1280	valid
1.1s	1091×	body	2560	valid
914.0ms	5839×	body	80	valid
441.0ms	2909×	body	80	nan
286.0ms	461×	body	640	valid
146.0ms	126×	body	5120	valid
107.0ms	226×	body	320	valid
25.0ms	98×	body	160	valid