Details

sample1.0s

Algorithm

intervals

Results

752.0ms	190×	body	80	valid
73.0ms	43×	body	2560	valid
43.0ms	85×	body	80	nan
19.0ms	25×	body	1280	valid
9.0ms	14×	body	640	valid
5.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite219.0ms

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:

119.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
63.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
123.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms	(- (* b_2 b_2) (* a c))
222.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	2001
3	2001
2	1029
1	379
0	158

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

132.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
33.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
3	2001
2	1302
1	445
0	178

prune972.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite153.0ms

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:

89.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
108.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	2001
3	2001
2	1029
1	379
0	158

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes358.0ms

Accuracy

82.2% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 32.9b

bsearch176.0ms

Steps

Iters	Range		Point
10	1.3859530517218358e-142	9.527435083115218e-125	9.354082991670835e-125
8	-4.336983712965787e+155	-6.488343844980391e+152	-9.088000531423294e+152

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	872×	body	1280	valid
880.0ms	5928×	body	80	valid
758.0ms	1071×	body	2560	valid
366.0ms	3004×	body	80	nan
259.0ms	471×	body	640	valid
122.0ms	109×	body	5120	valid
65.0ms	216×	body	320	valid
24.0ms	111×	body	160	valid