Details

sample89.0ms

Algorithm

intervals

Results

10.0ms	184×	body	80	valid
9.0ms	32×	body	2560	valid
7.0ms	30×	body	1280	valid
4.0ms	24×	body	640	valid
3.0ms	83×	body	80	nan
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite228.0ms

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:

127.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (* b_2 b_2) (* a c))
51.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
51.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
132.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1408	3549
done	5000	3001

prune567.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma b_2 b_2 (- (* c a)))
2.5b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
9.2b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
19.7b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1` `flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef`

Counts

4 → 186

Calls

4 calls:

1.0ms	(fma b_2 b_2 (- (* c a)))
68.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
3.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series662.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma b_2 b_2 (- (* c a)))
215.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
275.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
111.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.9s

Counts

198 → 198

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	295	5516
1	678	4787
2	2110	4608
done	5000	4543

prune764.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.5b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
0.8b	(fma b_2 b_2 (- (* c a)))
19.7b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

41.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
27.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0ms	(fma b_2 b_2 (- (* c a)))
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series570.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
120.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
66.0ms	(fma b_2 b_2 (- (* c a)))
111.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.6s

Counts

121 → 121

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	167	2224
1	334	1950
2	702	1731
3	1968	1653
done	5000	1598

prune511.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma b_2 b_2 (- (* c a)))
2.6b	(* (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
9.2b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
19.7b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
52×	`times-frac`
49×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/r*` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+` `fma-udef`

Counts

4 → 140

Calls

4 calls:

1.0ms	(fma b_2 b_2 (- (* c a)))
129.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
60.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
5.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma b_2 b_2 (- (* c a)))
245.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
293.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
78.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.6s

Counts

152 → 152

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	241	3394
1	627	2889
2	1945	2585
done	5000	2452

prune588.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

regimes151.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.6b

bsearch226.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.7151811081882383e+78
9	3.6976431258031608e-267	1.8292500652683027e-260	7.061692521831336e-266
8	-6.990724105819741e+111	-2.6156774686163576e+108	-5.674469085146397e+110

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.7151811081882383e+78

3.6976431258031608e-267

1.8292500652683027e-260

7.061692521831336e-266

-6.990724105819741e+111

-2.6156774686163576e+108

-5.674469085146397e+110

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	53
1	45	49
2	47	49
done	47	49

end0.0ms

sample3.1s

Algorithm

intervals

Results

538.0ms	1082×	body	2560	valid
492.0ms	5908×	body	80	valid
435.0ms	104×	body	160	valid
336.0ms	891×	body	1280	valid
336.0ms	3009×	body	80	nan
190.0ms	472×	body	640	valid
92.0ms	212×	body	320	valid
88.0ms	107×	body	5120	valid