Details

sample145.0ms

Algorithm

intervals

Results

51.0ms	184×	body	80	valid
8.0ms	32×	body	2560	valid
6.0ms	32×	body	1280	valid
3.0ms	84×	body	80	nan
3.0ms	16×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

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:

107.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
117.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
70.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1459
1	383
0	154

prune624.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.4b	(- (* b_2 b_2) (* c a))
24.6b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite159.0ms

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:

82.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
46.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
12.0ms	(- (* b_2 b_2) (* c a))
15.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
84.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
54.0ms	(- (* b_2 b_2) (* c a))
109.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1548
1	384
0	155

prune676.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
0.2b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.4b	(- (* b_2 b_2) (* c a))
24.6b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite122.0ms

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:

55.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
46.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
6.0ms	(- (* b_2 b_2) (* c a))
7.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
116.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
56.0ms	(- (* b_2 b_2) (* c a))
67.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify1.9s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	3117
1	641
0	259

prune680.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize70.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* c a))
1.4b	(- (* b_2 b_2) (* c a))
24.6b	(sqrt (- (* b_2 b_2) (* c a)))
24.6b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite59.0ms

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_2 b_2) (* c a))
12.0ms	(- (* b_2 b_2) (* c a))
14.0ms	(sqrt (- (* b_2 b_2) (* c a)))
19.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b_2 b_2) (* c a))
64.0ms	(- (* b_2 b_2) (* c a))
99.0ms	(sqrt (- (* b_2 b_2) (* c a)))
92.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.2s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3102
2	623
1	156
0	59

prune500.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.7b

regimes385.0ms

Accuracy

84.1% (4.5b remaining)

Error of 10.5b against oracle of 6.0b and baseline of 34.4b

bsearch118.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	3.1423118580081215e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample2.7s

Algorithm

intervals

Results

521.0ms	1043×	body	2560	valid
449.0ms	911×	body	1280	valid
449.0ms	5833×	body	80	valid
428.0ms	232×	body	320	valid
276.0ms	2878×	body	80	nan
120.0ms	449×	body	640	valid
51.0ms	102×	body	5120	valid
15.0ms	119×	body	160	valid