Details

sample166.0ms

Algorithm

intervals

Results

45.0ms	32×	body	1280	valid
19.0ms	185×	body	80	valid
18.0ms	33×	body	2560	valid
7.0ms	97×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite225.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

124.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
12.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
44.0ms	(- (* b_2 b_2) (* a c))
161.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
201.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	2015
3	2015
2	1393
1	494
0	199

prune801.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

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*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 200

Calls

4 calls:

43.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
55.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

212 → 212

Iterations

Iter	Nodes
done	2000
2	2000
1	742
0	303

prune743.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
507×	`add-sqr-sqrt`
420×	`*-un-lft-identity`
334×	`add-cube-cbrt`
86×	`difference-of-squares`
58×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
19×	`prod-diff`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 461

Calls

4 calls:

90.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
51.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

473 → 473

Iterations

Iter	Nodes
done	2000
2	2000
1	1843
0	632

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.6b	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
8×	`add-log-exp`
7×	`fma-neg`
6×	`pow1` `log-prod` `exp-sum`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`log-div` `sub-neg` `exp-diff` `sqrt-div` `diff-log` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `log-pow` `rem-exp-log`

Counts

4 → 100

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
33.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
133.0ms	(exp (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify826.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	2002
3	2002
2	893
1	366
0	166

prune459.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

regimes405.0ms

Accuracy

83.4% (4.5b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 33.0b

bsearch147.0ms

Steps

Iters	Range		Point
9	2.0671083276743448e-101	1.4914771383599542e-96	3.5014024016497154e-97
5	-1.4698287087051062e+86	-6.898352246976959e+85	-9.711132829713123e+85

simplify22.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample4.0s

Algorithm

intervals

Results

934.0ms	1105×	body	2560	valid
929.0ms	845×	body	1280	valid
886.0ms	5934×	body	80	valid
365.0ms	2937×	body	80	nan
255.0ms	435×	body	640	valid
107.0ms	120×	body	5120	valid
102.0ms	211×	body	320	valid
24.0ms	113×	body	160	valid