Details

sample116.0ms

Algorithm

intervals

Results

31.0ms	183×	body	80	valid
31.0ms	41×	body	2560	valid
17.0ms	31×	body	1280	valid
9.0ms	84×	body	80	nan
5.0ms	12×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
20.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
22.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
10.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (* -4 a) c (* b b))
91.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
77.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
81.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.8s

Counts

179 → 179

Iterations

Iter	Nodes
done	5004
3	3721
2	1190
1	497
0	222

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
0.1b	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
20.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
10×	`fma-neg`
8×	`div-exp` `add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `flip3--` `div-inv` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `diff-log` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 290

Calls

4 calls:

25.0ms	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
31.0ms	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
26.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
154.0ms	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
117.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
110.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.2s

Counts

302 → 302

Iterations

Iter	Nodes
done	5000
2	1985
1	801
0	340

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (* a (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b)))))))
0.2b	(* a (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
20.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
60×	`prod-diff` `add-cube-cbrt`
48×	`add-exp-log`
37×	`sqrt-prod`
27×	`associate-r`
26×	`times-frac`
25×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
10×	`pow1` `fma-neg`
9×	`rec-exp` `1-exp`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`flip3--` `diff-log` `pow-prod-down` `associate-*r/` `un-div-inv` `div-inv` `pow-flip` `flip--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `-commutative` `inv-pow`

Counts

4 → 203

Calls

4 calls:

24.0ms	(/ 1 (* a (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b)))))))
45.0ms	(* a (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
10.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (* a (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b)))))))
241.0ms	(* a (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
107.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
104.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.0s

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
3	4256
2	1525
1	652
0	275

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
0.2b	(/ (/ 1 a) (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
20.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

918×	`times-frac`
597×	`add-sqr-sqrt`
596×	`*-un-lft-identity`
408×	`add-cube-cbrt`
94×	`distribute-lft-out--` `difference-of-squares`
80×	`sqrt-prod`
68×	`distribute-rgt-neg-in`
60×	`prod-diff`
48×	`add-exp-log`
44×	`div-inv`
34×	`associate-/r*` `div-exp`
31×	`associate-/r/`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube`
16×	`flip3--` `flip--` `associate-/l*`
10×	`fma-neg`
9×	`cbrt-undiv` `rec-exp` `1-exp`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 585

Calls

4 calls:

30.0ms	(/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
38.0ms	(/ (/ 1 a) (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
16.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
154.0ms	(/ (/ 1 a) (/ 1 (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
108.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
123.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.6s

Counts

597 → 597

Iterations

Iter	Nodes
done	5008
2	4159
1	1959
0	672

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

regimes425.0ms

Accuracy

82.9% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 32.9b

bsearch220.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	7.052614559736995e+62
8	-9.498395151376604e-61	-6.25213087380725e-65	-1.6239127264630285e-63

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.1s	1101×	body	2560	valid
1.0s	856×	body	1280	valid
914.0ms	5893×	body	80	valid
423.0ms	3007×	body	80	nan
386.0ms	98×	body	5120	valid
294.0ms	463×	body	640	valid
109.0ms	216×	body	320	valid
29.0ms	119×	body	160	valid