Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	179×	body	80	valid
6.0ms	38×	body	1280	valid
4.0ms	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

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7
done	49	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

71.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
41.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063
done	5002	2063

prune553.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

88.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
35.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5002	1940
done	5002	1940

prune323.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

71.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063
done	5002	2063

prune326.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Counts

153 → 153

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	369	2606
1	1197	1735
2	5001	1648
done	5001	1648

prune336.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.9b

regimes336.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 33.8b

bsearch83.0ms

Steps

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

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	17
1	44	17
2	44	17
done	44	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

202.0ms	1024×	body	2560	valid
195.0ms	5915×	body	80	valid
144.0ms	899×	body	1280	valid
86.0ms	2902×	body	80	nan
54.0ms	449×	body	640	valid
28.0ms	117×	body	5120	valid
22.0ms	236×	body	320	valid
8.0ms	129×	body	160	valid