Details

sample125.0ms

Algorithm

intervals

Results

38.0ms	41×	body	2560	valid
25.0ms	183×	body	80	valid
21.0ms	31×	body	1280	valid
10.0ms	84×	body	80	nan
7.0ms	12×	body	640	valid
4.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize62.0ms

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))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite943.0ms

Algorithm

rewrite-expression-head

Rules

587×	`add-sqr-sqrt`
380×	`prod-diff`
326×	`*-un-lft-identity`
210×	`add-cube-cbrt`
192×	`sqrt-prod`
132×	`associate-l`
130×	`difference-of-squares`
112×	`unswap-sqr`
84×	`associate-r`
68×	`distribute-rgt-neg-in`
63×	`distribute-lft-neg-in` `swap-sqr`
58×	`distribute-lft-out--`
52×	`*-commutative`
25×	`fma-neg`
21×	`neg-mul-1` `times-frac`
10×	`add-log-exp`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `div-inv`

Counts

4 → 537

Calls

4 calls:

532.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (* b_2 b_2) (* a c))
192.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

549 → 549

Iterations

Iter	Nodes
done	5001
2	2861
1	1223
0	542

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite909.0ms

Algorithm

rewrite-expression-head

Rules

685×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
380×	`prod-diff`
272×	`add-cube-cbrt`
201×	`sqrt-prod`
165×	`times-frac`
148×	`difference-of-squares`
132×	`associate-l`
112×	`unswap-sqr`
84×	`associate-r`
77×	`distribute-rgt-neg-in`
76×	`distribute-lft-out--`
63×	`distribute-lft-neg-in` `swap-sqr`
52×	`*-commutative`
34×	`associate-/r*`
25×	`fma-neg`
21×	`neg-mul-1` `associate-/r/`
15×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--` `associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `clear-num` `diff-log`
2×	`rec-exp` `sub-neg` `frac-2neg` `sqrt-div` `1-exp` `remove-double-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 636

Calls

4 calls:

515.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
60.0ms	(- (* b_2 b_2) (* a c))
168.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
120.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
52.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

648 → 648

Iterations

Iter	Nodes
done	5014
2	3732
1	1512
0	655

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite990.0ms

Algorithm

rewrite-expression-head

Rules

1085×	`add-sqr-sqrt`
897×	`times-frac`
824×	`*-un-lft-identity`
552×	`add-cube-cbrt`
380×	`prod-diff`
231×	`sqrt-prod`
208×	`difference-of-squares`
136×	`distribute-lft-out--`
132×	`associate-l`
112×	`unswap-sqr`
107×	`distribute-rgt-neg-in`
84×	`associate-r`
63×	`distribute-lft-neg-in` `swap-sqr`
52×	`*-commutative`
44×	`add-exp-log`
43×	`div-inv`
41×	`associate-/r/`
37×	`associate-/r*`
32×	`div-exp`
25×	`fma-neg`
21×	`neg-mul-1`
19×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
10×	`add-log-exp`
9×	`associate-/l/`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 933

Calls

4 calls:

526.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
60.0ms	(- (* b_2 b_2) (* a c))
173.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
126.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
58.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

945 → 945

Iterations

Iter	Nodes
done	5002
1	2706
0	988

prune3.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

1244×	`add-sqr-sqrt`
780×	`prod-diff`
637×	`*-un-lft-identity`
529×	`sqrt-prod`
372×	`add-cube-cbrt`
324×	`difference-of-squares`
255×	`unswap-sqr`
225×	`associate-l`
202×	`distribute-rgt-in` `distribute-lft-in`
185×	`distribute-rgt-neg-in`
183×	`distribute-lft-neg-in`
132×	`distribute-lft-out--`
103×	`swap-sqr`
93×	`*-commutative`
91×	`associate-r`
61×	`neg-mul-1`
25×	`fma-neg`
18×	`frac-times`
13×	`flip3--` `add-exp-log` `flip--`
11×	`times-frac`
10×	`add-log-exp`
9×	`associate-/r` `add-cbrt-cube` `associate-l/` `associate-/l*`
7×	`pow1`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `diff-log`
2×	`sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `div-inv`

Counts

4 → 961

Calls

4 calls:

603.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
86.0ms	(- (* b_2 b_2) (* a c))
163.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
49.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

973 → 973

Iterations

Iter	Nodes
done	5000
2	4613
1	2304
0	807

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

regimes320.0ms

Accuracy

82.6% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 33.1b

bsearch177.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	7.052614559736995e+62
8	-9.498395151376604e-61	-6.25213087380725e-65	-1.6239127264630285e-63

simplify8.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	1104×	body	2560	valid
736.0ms	854×	body	1280	valid
681.0ms	5893×	body	80	valid
353.0ms	3005×	body	80	nan
223.0ms	463×	body	640	valid
87.0ms	221×	body	320	valid
70.0ms	98×	body	5120	valid
22.0ms	115×	body	160	valid