Details

sample165.0ms

Algorithm

intervals

Results

47.0ms	187×	body	80	valid
38.0ms	36×	body	2560	valid
22.0ms	25×	body	1280	valid
15.0ms	86×	body	80	nan
12.0ms	17×	body	640	valid
4.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify139.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
0.8b	(- (* b b) (* (* c a) 4))
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
23.5b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite124.0ms

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:

72.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
7.0ms	(- (* b b) (* (* c a) 4))
32.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
12.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
78.0ms	(- (* b b) (* (* c a) 4))
100.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
95.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.6s

Counts

100 → 100

Iterations

Iter	Nodes
3	3565
2	1088
1	398
0	161

prune553.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
0.8b	(- (* b b) (* (* c a) 4))
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
23.5b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite230.0ms

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:

147.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
15.0ms	(- (* b b) (* (* c a) 4))
59.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
75.0ms	(- (* b b) (* (* c a) 4))
132.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
90.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify4.0s

Counts

101 → 101

Iterations

Iter	Nodes
3	5062
2	1496
1	461
0	181

prune435.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.9b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
23.5b	(sqrt (- (* b b) (* (* c a) 4)))
23.5b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

40.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
64.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
16.0ms	(sqrt (- (* b b) (* (* c a) 4)))
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
123.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
128.0ms	(sqrt (- (* b b) (* (* c a) 4)))
125.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify4.2s

Counts

76 → 76

Iterations

Iter	Nodes
4	6256
3	1938
2	598
1	193
0	82

prune610.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

localize47.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (* (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4)))) (cbrt (- (* b b) (* (* c a) 4)))))
24.2b	(cbrt (- (* b b) (* (* c a) 4)))
24.2b	(cbrt (- (* b b) (* (* c a) 4)))
24.2b	(cbrt (- (* b b) (* (* c a) 4)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

129.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4)))) (cbrt (- (* b b) (* (* c a) 4)))))
5.0ms	(cbrt (- (* b b) (* (* c a) 4)))
5.0ms	(cbrt (- (* b b) (* (* c a) 4)))
5.0ms	(cbrt (- (* b b) (* (* c a) 4)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4)))) (cbrt (- (* b b) (* (* c a) 4)))))
118.0ms	(cbrt (- (* b b) (* (* c a) 4)))
126.0ms	(cbrt (- (* b b) (* (* c a) 4)))
137.0ms	(cbrt (- (* b b) (* (* c a) 4)))

simplify3.6s

Counts

105 → 105

Iterations

Iter	Nodes
4	6260
3	1914
2	722
1	343
0	188

prune605.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.4b

regimes437.0ms

Accuracy

84.1% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 32.9b

bsearch225.0ms

Steps

Iters	Range		Point
8	5.833527798943191e-77	3.6732813120885656e-72	3.1295384133612364e-73
9	-2.2174027590176242e+73	-8.164533525332822e+65	-3.063397748446981e+71

simplify5.0ms

Iterations

Iter	Nodes
2	34
1	34
0	29

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.9s	1026×	body	2560	valid
924.0ms	5891×	body	80	valid
726.0ms	881×	body	1280	valid
407.0ms	2954×	body	80	nan
366.0ms	464×	body	640	valid
195.0ms	237×	body	320	valid
136.0ms	96×	body	5120	valid
27.0ms	104×	body	160	valid