Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	32×	body	2560	valid
10.0ms	184×	body	80	valid
8.0ms	31×	body	1280	valid
4.0ms	84×	body	80	nan
4.0ms	17×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify131.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	72
2	42
1	24
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
0.2b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite173.0ms

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--` `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 → 84

Calls

4 calls:

84.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
66.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
12.0ms	(- (* b b) (* (* c a) 4.0))
10.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
123.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
77.0ms	(- (* b b) (* (* c a) 4.0))
82.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1180
1	391
0	158

prune632.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize50.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* c a) 4.0))
1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

12.0ms	(- (* b b) (* (* c a) 4.0))
13.0ms	(- (* b b) (* (* c a) 4.0))
14.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
12.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* b b) (* (* c a) 4.0))
71.0ms	(- (* b b) (* (* c a) 4.0))
98.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
135.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	2061
2	502
1	157
0	62

prune672.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize118.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite45.0ms

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` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (* b b) (* (* c a) 4.0))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
13.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
17.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* c a) 4.0))
87.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
120.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
103.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.9s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	2061
2	502
1	157
0	62

prune543.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

localize45.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (* (* (cbrt (- (* b b) (* (* c a) 4.0))) (cbrt (- (* b b) (* (* c a) 4.0)))) (cbrt (- (* b b) (* (* c a) 4.0)))))
25.5b	(cbrt (- (* b b) (* (* c a) 4.0)))
25.5b	(cbrt (- (* b b) (* (* c a) 4.0)))
25.5b	(cbrt (- (* b b) (* (* c a) 4.0)))

rewrite162.0ms

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` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

126.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* c a) 4.0))) (cbrt (- (* b b) (* (* c a) 4.0)))) (cbrt (- (* b b) (* (* c a) 4.0)))))
9.0ms	(cbrt (- (* b b) (* (* c a) 4.0)))
13.0ms	(cbrt (- (* b b) (* (* c a) 4.0)))
5.0ms	(cbrt (- (* b b) (* (* c a) 4.0)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* c a) 4.0))) (cbrt (- (* b b) (* (* c a) 4.0)))) (cbrt (- (* b b) (* (* c a) 4.0)))))
122.0ms	(cbrt (- (* b b) (* (* c a) 4.0)))
116.0ms	(cbrt (- (* b b) (* (* c a) 4.0)))
167.0ms	(cbrt (- (* b b) (* (* c a) 4.0)))

simplify2.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	5006
3	1978
2	732
1	351
0	189

prune708.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.8b

regimes515.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.6b against oracle of 6.2b and baseline of 34.4b

bsearch178.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	2.8983489306952693e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify11.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	5835×	body	80	valid
780.0ms	906×	body	1280	valid
581.0ms	1040×	body	2560	valid
320.0ms	2881×	body	80	nan
134.0ms	456×	body	640	valid
80.0ms	116×	body	160	valid
62.0ms	102×	body	5120	valid
50.0ms	232×	body	320	valid