Details

sample85.0ms

Algorithm

intervals

Results

51.0ms	272×	body	80	valid
16.0ms	85×	body	80	nan

simplify193.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	170
7	170
6	168
5	164
4	157
3	132
2	76
1	39
0	20

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize172.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma c (* a -4) (* b b))) b)
1.2b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
22.9b	(sqrt (fma c (* a -4) (* b b)))
22.9b	(sqrt (fma c (* a -4) (* b b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

15.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
21.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
2.0ms	(sqrt (fma c (* a -4) (* b b)))
6.0ms	(sqrt (fma c (* a -4) (* b b)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
115.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
91.0ms	(sqrt (fma c (* a -4) (* b b)))
156.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.3s

Counts

177 → 177

Iterations

Iter	Nodes
done	2000
3	2000
2	995
1	426
0	194

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.3b

localize152.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma c (* a -4) (* b b))) b)
3.4b	(* (/ a b) c)
4.6b	(/ (* 2 (- (* (/ a b) c) b)) (* 2 a))
22.9b	(sqrt (fma c (* a -4) (* b b)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff`
16×	`sqrt-prod`
13×	`associate-l`
11×	`times-frac`
7×	`pow1`
6×	`fma-neg` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r`
2×	`flip3--` `associate-*r/` `div-inv` `flip--` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `associate-/l` `distribute-lft-out--`

Counts

4 → 119

Calls

4 calls:

16.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
14.0ms	(* (/ a b) c)
44.0ms	(/ (* 2 (- (* (/ a b) c) b)) (* 2 a))
1.0ms	(sqrt (fma c (* a -4) (* b b)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
38.0ms	(* (/ a b) c)
67.0ms	(/ (* 2 (- (* (/ a b) c) b)) (* 2 a))
97.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	2008
3	2008
2	1858
1	509
0	203

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize143.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ c b) (/ b a))
0.1b	(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
0.9b	(- (sqrt (fma c (* a -4) (* b b))) b)
22.9b	(sqrt (fma c (* a -4) (* b b)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

387×	`times-frac`
336×	`add-sqr-sqrt`
303×	`*-un-lft-identity`
271×	`add-cube-cbrt`
187×	`prod-diff`
32×	`div-inv`
30×	`difference-of-squares`
28×	`sqrt-prod`
22×	`associate-/r*`
19×	`fma-neg`
15×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/r/` `frac-sub`

Counts

4 → 371

Calls

4 calls:

19.0ms	(- (/ c b) (/ b a))
12.0ms	(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
13.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (/ c b) (/ b a))
255.0ms	(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
143.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
128.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.5s

Counts

383 → 383

Iterations

Iter	Nodes
done	2003
2	2003
1	1348
0	562

prune6.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

localize162.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) c)
0.4b	(/ 1 (/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) c))
0.9b	(- (sqrt (fma c (* a -4) (* b b))) b)
22.9b	(sqrt (fma c (* a -4) (* b b)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

828×	`times-frac`
562×	`add-sqr-sqrt`
463×	`*-un-lft-identity`
365×	`add-cube-cbrt`
98×	`difference-of-squares`
73×	`associate-/r*`
64×	`sqrt-prod`
49×	`distribute-lft-out--`
30×	`add-exp-log`
25×	`associate-/l*`
22×	`div-inv`
18×	`add-cbrt-cube` `div-exp` `prod-diff`
9×	`cbrt-undiv`
6×	`pow1` `fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `div-sub`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-/r/` `pow-flip` `flip--` `inv-pow` `associate-/l/`

Counts

4 → 479

Calls

4 calls:

36.0ms	(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) c)
27.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) c))
13.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) c)
291.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) c))
120.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
122.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.0s

Counts

491 → 491

Iterations

Iter	Nodes
done	2002
2	2002
1	1645
0	604

prune7.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.2b

regimes410.0ms

Accuracy

91.5% (0.7b remaining)

Error of 12.6b against oracle of 11.9b and baseline of 20.2b

bsearch296.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
7	-1.1161865709419737e-308	6.1382423128657715e-307	2.01827746078287e-310

simplify26.0ms

Iterations

Iter	Nodes
done	41
1	41
0	38

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.9s	8671×	body	80	valid
524.0ms	2938×	body	80	nan