Details

sample200.0ms

Algorithm

intervals

Results

19.0ms	192×	body	80	valid
19.0ms	37×	body	2560	valid
12.0ms	30×	body	1280	valid
6.0ms	81×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

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:

89.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify717.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1459
1	384
0	154

prune531.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
0.4b	(- (pow b_2 2) (* a c))
1.2b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
22.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 162

Calls

4 calls:

123.0ms	(/ 1 (/ a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
25.0ms	(- (pow b_2 2) (* a c))
71.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
18.0ms	(sqrt (- (pow b_2 2) (* a c)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ 1 (/ a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
58.0ms	(- (pow b_2 2) (* a c))
113.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
102.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.5s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	3515
1	621
0	257

prune644.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
1.2b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
22.4b	(sqrt (- (* b_2 b_2) (* c a)))
22.4b	(sqrt (- (pow b_2 2) (* a c)))

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` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

55.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
42.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* c a)))
21.0ms	(sqrt (- (pow b_2 2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
103.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
89.0ms	(sqrt (- (* b_2 b_2) (* c a)))
81.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify2.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	4690
2	981
1	286
0	124

prune618.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
22.4b	(sqrt (- (pow b_2 2) (* a c)))
22.4b	(sqrt (- (pow b_2 2) (* a c)))
22.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`*-un-lft-identity`
7×	`pow1` `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`
2×	`difference-of-squares`
1×	`sub-neg` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

57.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
11.0ms	(sqrt (- (pow b_2 2) (* a c)))
15.0ms	(sqrt (- (pow b_2 2) (* a c)))
12.0ms	(sqrt (- (pow b_2 2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
84.0ms	(sqrt (- (pow b_2 2) (* a c)))
98.0ms	(sqrt (- (pow b_2 2) (* a c)))
97.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2685
2	623
1	180
0	78

prune589.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.0b

regimes604.0ms

Accuracy

82.8% (5.0b remaining)

Error of 10.8b against oracle of 5.9b and baseline of 34.7b

bsearch181.0ms

Steps

Iters	Range		Point
8	6.341672394037201e-140	1.4419175235777254e-136	1.423163788076293e-136
8	-1.0455781936591884e+110	-3.8601914758440924e+107	-3.828737593568667e+109

simplify3.0ms

Iterations

Iter	Nodes
done	36
1	36
0	33

end0.0ms

sample2.9s

Algorithm

intervals

Results

867.0ms	5835×	body	80	valid
516.0ms	1071×	body	2560	valid
422.0ms	935×	body	1280	valid
311.0ms	2813×	body	80	nan
111.0ms	454×	body	640	valid
92.0ms	94×	body	5120	valid
53.0ms	115×	body	160	valid
39.0ms	222×	body	320	valid