Details

sample146.0ms

Algorithm

intervals

Results

41.0ms	184×	body	80	valid
31.0ms	35×	body	2560	valid
21.0ms	28×	body	1280	valid
12.0ms	86×	body	80	nan
9.0ms	15×	body	640	valid
5.0ms	4×	body	5120	valid
4.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify125.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.8b	(fma b b (* (* a -4) c))
1.7b	(- (sqrt (fma b b (* (* a -4) c))) b)
24.6b	(sqrt (fma b b (* (* a -4) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

17.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms	(fma b b (* (* a -4) c))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
59.0ms	(fma b b (* (* a -4) c))
135.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
103.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
3	2689
2	950
1	405
0	180

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c (* -4 a) (* b b))
0.1b	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
1.7b	(- (sqrt (fma c (* -4 a) (* b b))) b)
24.6b	(sqrt (fma c (* -4 a) (* b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
28.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
10.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma c (* -4 a) (* b b))
110.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
142.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
129.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify5.0s

Counts

126 → 126

Iterations

Iter	Nodes
4	6613
3	1992
2	726
1	321
0	157

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.7b	(- (sqrt (fma c (* -4 a) (* b b))) b)
24.6b	(sqrt (fma c (* -4 a) (* b b)))
24.6b	(sqrt (fma c (* -4 a) (* b b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

16.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
16.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms	(sqrt (fma c (* -4 a) (* b b)))
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
124.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
136.0ms	(sqrt (fma c (* -4 a) (* b b)))
111.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
4	2478
3	903
2	292
1	153
0	85

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize41.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.7b	(- (sqrt (fma c (* -4 a) (* b b))) b)
24.6b	(sqrt (fma c (* -4 a) (* b b)))
24.6b	(sqrt (fma c (* -4 a) (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
13.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
105.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
104.0ms	(sqrt (fma c (* -4 a) (* b b)))
115.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
4	2478
3	903
2	292
1	153
0	85

prune2.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes420.0ms

Accuracy

84.4% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.4b

bsearch239.0ms

Steps

Iters	Range		Point
10	8.296670056881522e-85	2.5972983117194536e-74	2.326372645943808e-74
7	-1.8217288728729631e+111	-6.606823090402082e+109	-1.0027271082217074e+110

simplify5.0ms

Iterations

Iter	Nodes
2	29
1	29
0	26

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.4s	5836×	body	80	valid
1.2s	1126×	body	2560	valid
858.0ms	915×	body	1280	valid
545.0ms	236×	body	320	valid
417.0ms	2976×	body	80	nan
287.0ms	417×	body	640	valid
146.0ms	119×	body	5120	valid
33.0ms	115×	body	160	valid