Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	196×	body	80	valid
8.0ms	27×	body	2560	valid
7.0ms	31×	body	1280	valid
5.0ms	92×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify130.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.9b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

132.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
63.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
121.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
83.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

118 → 118

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	195	2476
1	521	2183
2	2492	1866
done	5000	1798

prune544.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.9b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

81.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
58.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
132.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

164 → 164

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	261	4025
1	674	3498
2	3234	3147
done	5000	3070

prune551.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

24.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify956.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (138.0ms)

Iter	Nodes	Cost
0	71	1146
1	185	1058
2	843	952
done	5000	952

prune572.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
1.2b	(- (* b b) (* (* 4.0 a) c))
5.6b	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac`
71×	`prod-diff`
57×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
33×	`sqrt-prod`
21×	`div-inv`
11×	`fma-neg`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `associate-/r*` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

25.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
62.0ms	(- (* b b) (* (* 4.0 a) c))
177.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

176 → 176

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	275	6226
1	694	5352
2	2788	4572
done	5000	4252

prune583.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes358.0ms

Accuracy

85.3% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.5b

bsearch136.0ms

Steps

Iters	Range		Point
5	6.945766558749631e-52	1.7836275468166073e-51	8.70366778308292e-52
8	-1.5489453231745737e+155	-2.021963087226922e+151	-2.2976245343188767e+152

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	42
1	32	42
done	32	42

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	5754×	body	80	valid
624.0ms	1069×	body	2560	valid
423.0ms	917×	body	1280	valid
253.0ms	2912×	body	80	nan
194.0ms	488×	body	640	valid
58.0ms	109×	body	5120	valid
55.0ms	246×	body	320	valid
53.0ms	91×	body	160	valid