Details

sample119.0ms

Algorithm

intervals

Results

28.0ms	92×	body	80	nan
19.0ms	33×	body	2560	valid
17.0ms	181×	body	80	valid
12.0ms	27×	body	1280	valid
5.0ms	13×	body	640	valid
3.0ms	4×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify440.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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: 33.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite265.0ms

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:

160.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
11.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
74.0ms	(- (* b b) (* (* 4.0 a) c))
131.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

118 → 118

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	195	2476
1	521	2183
2	2396	1862
done	5000	1794

prune457.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

172.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
11.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
50.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

127 → 127

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	221	2739
1	593	2382
2	3109	1975
done	5001	1901

prune493.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

localize33.0ms

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)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite247.0ms

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:

105.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

128 → 128

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	113	2856
1	295	2330
2	1225	1950
done	5001	1810

prune593.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

localize47.0ms

Local error

Found 4 expressions with local error:

21.8b	(fma (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

1.0ms	(fma (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
34.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(fma (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
135.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

73 → 73

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	71	1425
1	173	1318
2	644	939
3	3756	906
done	5000	903

prune423.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 5.2b

regimes361.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 34.0b

bsearch134.0ms

Steps

Iters	Range		Point
7	1.2976235572645919e-73	6.718394677208045e-72	4.089744618622775e-73
7	-4.1637922183371475e+115	-1.3908068482385633e+114	-3.028200009108188e+115

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	36
1	30	36
done	30	36

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	5893×	body	80	valid
672.0ms	1092×	body	2560	valid
435.0ms	848×	body	1280	valid
365.0ms	3047×	body	80	nan
218.0ms	463×	body	640	valid
55.0ms	96×	body	5120	valid
53.0ms	235×	body	320	valid
18.0ms	105×	body	160	valid