Details

sample40.0ms

Algorithm

intervals

Results

7.0ms	179×	body	80	valid
6.0ms	38×	body	1280	valid
5.0ms	24×	body	2560	valid
2.0ms	73×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9
done	164	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

81.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128
done	5002	2128

prune338.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

110.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms	(- (* b b) (* 4.0 (* a c)))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
51.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	656	3422
1	2594	2238
2	5001	2193
done	5001	2193

prune333.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

82.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(- (* b b) (* 4.0 (* a c)))
32.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128
done	5002	2128

prune348.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
11.4b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`fma-neg` `prod-diff`
10×	`add-log-exp`
6×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	313	1367
1	1139	1090
2	5001	1064
done	5001	1064

prune350.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

regimes297.0ms

Accuracy

84.5% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 33.9b

bsearch102.0ms

Steps

Iters	Range		Point
9	1.4800420954007604e+99	2.6367850541344314e+108	1.2959095079224867e+107
8	-4.0980741083472165e-57	-1.167522134822322e-60	-4.8253306290577406e-58

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16
done	36	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

226.0ms	1023×	body	2560	valid
223.0ms	5918×	body	80	valid
163.0ms	896×	body	1280	valid
103.0ms	2904×	body	80	nan
62.0ms	451×	body	640	valid
31.0ms	117×	body	5120	valid
24.0ms	234×	body	320	valid
9.0ms	129×	body	160	valid