Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
6.0ms	36×	body	1280	valid
6.0ms	165×	body	80	valid
3.0ms	87×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

38.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
46.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify898.0ms

Counts

195 → 195

Iterations

Useful iterations: done (891.0ms)

Iter	Nodes	Cost
0	321	4967
1	751	4592
2	2601	4265
done	5000	4264

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b) (/ (/ 1 2.0) a))
1.3b	(fma b b (- (* (* 4.0 a) c)))
1.6b	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
22.6b	(sqrt (fma b b (- (* (* 4.0 a) c))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`times-frac`
60×	`*-un-lft-identity`
55×	`add-cube-cbrt`
43×	`associate-r`
19×	`add-exp-log`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `div-exp` `associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `flip3--` `flip--` `cbrt-unprod`
2×	`frac-times` `associate-*l/` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `fma-udef`

Counts

4 → 143

Calls

4 calls:

38.0ms	(* (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b) (/ (/ 1 2.0) a))
0.0ms	(fma b b (- (* (* 4.0 a) c)))
6.0ms	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
1.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b) (/ (/ 1 2.0) a))
55.0ms	(fma b b (- (* (* 4.0 a) c)))
89.0ms	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
80.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))

simplify942.0ms

Counts

155 → 155

Iterations

Useful iterations: done (938.0ms)

Iter	Nodes	Cost
0	284	3455
1	717	2972
2	2347	2574
done	5001	2565

prune398.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac`
452×	`add-sqr-sqrt`
377×	`*-un-lft-identity`
303×	`add-cube-cbrt`
74×	`difference-of-squares`
71×	`associate-/r*`
52×	`sqrt-prod`
37×	`distribute-lft-out--`
25×	`add-exp-log`
19×	`prod-diff`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 388

Calls

4 calls:

35.0ms	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

400 → 400

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	612	12852
1	1428	11390
2	4640	10543
done	5000	10543

prune820.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

23.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
26.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
78.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify929.0ms

Counts

128 → 128

Iterations

Useful iterations: done (925.0ms)

Iter	Nodes	Cost
0	113	2856
1	262	2310
2	899	1912
done	5000	1702

prune355.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes192.0ms

Accuracy

81.5% (5.2b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 33.8b

bsearch113.0ms

Steps

Iters	Range		Point
9	2.365685850767504e-168	1.2053288471691685e-161	1.1860189201379418e-161
8	-1.4395777107888637e+138	-2.299948591329529e+133	-1.9827654008890006e+134

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	39	40
2	47	40
done	47	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

233.0ms	5914×	body	80	valid
230.0ms	1025×	body	2560	valid
159.0ms	891×	body	1280	valid
106.0ms	2997×	body	80	nan
69.0ms	450×	body	640	valid
29.0ms	107×	body	5120	valid
22.0ms	209×	body	320	valid
7.0ms	104×	body	160	valid