Details

sample398.0ms

Algorithm

intervals

Results

76.0ms	176×	body	80	valid
33.0ms	42×	body	2560	valid
15.0ms	23×	body	1280	valid
15.0ms	23×	body	640	valid
12.0ms	98×	body	80	nan
4.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize42.0ms

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))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite168.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

78.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
90.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
3	2004
2	1521
1	578
0	248

prune742.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

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×	`associate-r` `add-exp-log`
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` `insert-posit16` `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×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 173

Calls

4 calls:

80.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
16.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
46.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

185 → 185

Iterations

Iter	Nodes
done	2011
3	2011
2	1654
1	640
0	267

prune658.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize30.0ms

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))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

66.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
61.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
3	2004
2	1521
1	578
0	248

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b	(- (* b_2 b_2) (* a c))
6.2b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `div-exp` `frac-sub` `sub-div`

Counts

4 → 893

Calls

4 calls:

27.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
20.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

608.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
50.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
125.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

905 → 905

Iterations

Iter	Nodes
done	2000
1	2000
0	907

prune5.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

regimes536.0ms

Accuracy

83.4% (4.6b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 33.6b

bsearch140.0ms

Steps

Iters	Range		Point
7	6.52945691119865e+99	1.3360629297740576e+102	6.384705165981893e+101
9	-3.929467862544791e-84	-4.77908653107304e-89	-5.961198324014865e-88

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	26

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	1081×	body	2560	valid
672.0ms	5863×	body	80	valid
475.0ms	902×	body	1280	valid
238.0ms	2935×	body	80	nan
236.0ms	471×	body	640	valid
93.0ms	109×	body	5120	valid
57.0ms	218×	body	320	valid
19.0ms	115×	body	160	valid