Details

sample154.0ms

Algorithm

intervals

Results

49.0ms	3×	body	160	valid
13.0ms	37×	body	2560	valid
10.0ms	182×	body	80	valid
8.0ms	31×	body	1280	valid
5.0ms	22×	body	640	valid
5.0ms	89×	body	80	nan
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	valid

simplify66.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize106.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

126.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
49.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
124.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms	(- (* b_2 b_2) (* a c))
128.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2149
1	583
0	244

prune751.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
4.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 194

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
71.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b_2 b_2) (* a c))
215.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
253.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	4614
1	804
0	315

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
15.9b	(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `associate-/r/` `difference-of-squares` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

38.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series886.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms	(- (* b_2 b_2) (* a c))
666.0ms	(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	3484
1	526
0	196

prune625.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.0b

localize149.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

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×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	3185
2	595
1	169
0	67

prune606.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 5.0b

regimes466.0ms

Accuracy

83.2% (4.5b remaining)

Error of 10.5b against oracle of 6.0b and baseline of 32.7b

bsearch137.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	3.038903409991338e+107
9	-1.0952546209266604e-55	-7.034794544076098e-65	-9.332433396832084e-58

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	22

end0.0ms

sample2.6s

Algorithm

intervals

Results

715.0ms	891×	body	1280	valid
499.0ms	1019×	body	2560	valid
448.0ms	5889×	body	80	valid
257.0ms	2880×	body	80	nan
141.0ms	461×	body	640	valid
82.0ms	98×	body	5120	valid
36.0ms	223×	body	320	valid
12.0ms	117×	body	160	valid