Details

sample68.0ms

Algorithm

intervals

Results

15.0ms	35×	body	2560	valid
13.0ms	188×	body	80	valid
10.0ms	28×	body	1280	valid
6.0ms	85×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

129.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
8.0ms	(- (* b b) (* (* 3 a) c))
52.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
79.0ms	(- (* b b) (* (* 3 a) c))
126.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
94.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5013
2	1265
1	396
0	157

prune498.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 c) a))) b) (* 3 a))
0.8b	(- (* b b) (* (* 3 c) a))
1.6b	(- (sqrt (- (* b b) (* (* 3 c) a))) b)
21.2b	(sqrt (- (* b b) (* (* 3 c) a)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

94.0ms	(/ (- (sqrt (- (* b b) (* (* 3 c) a))) b) (* 3 a))
8.0ms	(- (* b b) (* (* 3 c) a))
50.0ms	(- (sqrt (- (* b b) (* (* 3 c) a))) b)
23.0ms	(sqrt (- (* b b) (* (* 3 c) a)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (sqrt (- (* b b) (* (* 3 c) a))) b) (* 3 a))
55.0ms	(- (* b b) (* (* 3 c) a))
112.0ms	(- (sqrt (- (* b b) (* (* 3 c) a))) b)
79.0ms	(sqrt (- (* b b) (* (* 3 c) a)))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5003
2	1281
1	402
0	158

prune504.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

15.0ms	(/ 1 (* 3 a))
10.0ms	(- (* b b) (* (* 3 a) c))
57.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (* 3 a))
54.0ms	(- (* b b) (* (* 3 a) c))
107.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
107.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	3410
2	920
1	326
0	140

prune446.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
0.8b	(- (* b b) (* (* 3 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

130.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
15.0ms	(- (* b b) (* (* 3 a) c))
71.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
59.0ms	(- (* b b) (* (* 3 a) c))
107.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
75.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1520
1	448
0	179

prune459.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.7b

regimes650.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.2b against oracle of 5.4b and baseline of 34.1b

bsearch153.0ms

Steps

Iters	Range		Point
6	1.5727591416233446e-143	1.789606490082599e-142	1.744031351412433e-142
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-1.4367588244629113e+152

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

924.0ms	5801×	body	80	valid
638.0ms	1082×	body	2560	valid
415.0ms	933×	body	1280	valid
359.0ms	2987×	body	80	nan
135.0ms	490×	body	640	valid
87.0ms	245×	body	320	valid
56.0ms	107×	body	5120	valid
17.0ms	123×	body	160	valid