Details

sample241.0ms

Algorithm

intervals

Results

21.0ms	39×	body	2560	valid
21.0ms	187×	body	80	valid
11.0ms	28×	body	1280	valid
8.0ms	89×	body	80	nan
3.0ms	10×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	34
5	34
4	32
3	30
2	23
1	15
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

79.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
49.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
38.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
3	3530
2	1175
1	462
0	199

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 123

Calls

4 calls:

126.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
36.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

135 → 135

Iterations

Iter	Nodes
3	4054
2	1372
1	527
0	219

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`prod-diff`
51×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-l` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 162

Calls

4 calls:

170.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
47.0ms	(- (* b_2 b_2) (* a c))
116.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

174 → 174

Iterations

Iter	Nodes
3	3932
2	1465
1	627
0	243

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

132 → 132

Iterations

Iter	Nodes
3	2134
2	669
1	257
0	112

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes363.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 33.6b

bsearch172.0ms

Steps

Iters	Range		Point
8	6.256891986679925e-86	3.543466061308676e-83	5.69412176017963e-84
10	-1.0499721897563905e+163	-8.354690034354516e+151	-4.1672202318347805e+152

simplify9.0ms

Iterations

Iter	Nodes
2	26
1	26
0	23

end0.0ms

sample4.1s

Algorithm

intervals

Results

929.0ms	934×	body	1280	valid
908.0ms	1107×	body	2560	valid
817.0ms	5846×	body	80	valid
727.0ms	2915×	body	80	nan
189.0ms	454×	body	640	valid
128.0ms	113×	body	5120	valid
67.0ms	210×	body	320	valid
27.0ms	112×	body	160	valid