Details

sample217.0ms

Algorithm

intervals

Results

12.0ms	196×	body	80	valid
9.0ms	27×	body	2560	valid
7.0ms	32×	body	1280	valid
5.0ms	91×	body	80	nan
3.0ms	15×	body	640	valid
2.0ms	5×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

101.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
67.0ms	(- (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)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
47.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

130 → 130

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	195	2408
1	492	2127
2	1981	1877
done	5000	1818

prune477.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
1.0b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.2b	(- (* b_2 b_2) (* c a))
22.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

129.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
76.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
20.0ms	(- (* b_2 b_2) (* c a))
24.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
100.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
45.0ms	(- (* b_2 b_2) (* c a))
97.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.5s

Counts

130 → 130

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	194	2408
1	491	2127
2	2006	1876
done	5000	1818

prune436.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)))
1.0b	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
1.5b	(fma b_2 b_2 (- (* a c)))
22.8b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `fma-udef` `inv-pow`

Counts

4 → 188

Calls

4 calls:

50.0ms	(/ 1 (/ a (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)))
18.0ms	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
1.0ms	(fma b_2 b_2 (- (* a c)))
3.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ 1 (/ a (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)))
152.0ms	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
46.0ms	(fma b_2 b_2 (- (* a c)))
114.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify2.1s

Counts

200 → 200

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	277	4616
1	655	3953
2	3481	3699
done	5002	3637

prune632.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize48.0ms

Local error

Found 4 expressions with local error:

1.5b	(fma b_2 b_2 (- (* a c)))
22.8b	(sqrt (fma b_2 b_2 (- (* a c))))
22.8b	(sqrt (fma b_2 b_2 (- (* a c))))
22.8b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

1.0ms	(fma b_2 b_2 (- (* a c)))
14.0ms	(sqrt (fma b_2 b_2 (- (* a c))))
3.0ms	(sqrt (fma b_2 b_2 (- (* a c))))
3.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma b_2 b_2 (- (* a c)))
130.0ms	(sqrt (fma b_2 b_2 (- (* a c))))
118.0ms	(sqrt (fma b_2 b_2 (- (* a c))))
105.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify3.3s

Counts

67 → 67

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	44	711
1	82	642
2	208	604
3	847	601
4	4864	598
done	5000	598

prune345.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.6b

regimes336.0ms

Accuracy

85.2% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 34.4b

bsearch94.0ms

Steps

Iters	Range		Point
5	6.945766558749631e-52	1.7836275468166073e-51	8.70366778308292e-52
8	-1.5489453231745737e+155	-2.021963087226922e+151	-2.0907318212469142e+152

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	35
1	26	35
done	26	35

end0.0ms

sample2.9s

Algorithm

intervals

Results

852.0ms	5751×	body	80	valid
604.0ms	1069×	body	2560	valid
387.0ms	918×	body	1280	valid
245.0ms	2906×	body	80	nan
179.0ms	494×	body	640	valid
53.0ms	111×	body	5120	valid
42.0ms	239×	body	320	valid
11.0ms	94×	body	160	valid