Details

sample183.0ms

Algorithm

intervals

Results

20.0ms	191×	body	80	valid
15.0ms	28×	body	2560	valid
12.0ms	26×	body	1280	valid
7.0ms	82×	body	80	nan
6.0ms	19×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify190.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize145.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `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 → 95

Calls

4 calls:

195.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (* b_2 b_2) (* a c))
54.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
57.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
131.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify6.7s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
3	3529
2	1038
1	388
0	162

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize115.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite636.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`associate-/r/` `sqrt-prod`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`insert-posit16`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 131

Calls

4 calls:

150.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
293.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
158.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.1s

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
328.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
421.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
153.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.9s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	2093
1	612
0	241

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.7b

localize154.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.6b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.7b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite628.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`associate-r`
22×	`times-frac`
18×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--`
3×	`associate-/r` `flip3--` `associate-l*` `flip--`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

158.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
324.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
102.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.0s

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
444.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
307.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1758
1	536
0	207

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.7b

localize140.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.9b	(/ a (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite547.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`div-exp`
14×	`add-sqr-sqrt`
13×	`prod-exp`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`pow1` `cbrt-undiv`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`associate-/r/` `cbrt-unprod`
4×	`rec-exp` `flip3--` `1-exp` `sqrt-prod` `insert-posit16` `flip--`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-r/` `div-inv` `pow-flip` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 96

Calls

4 calls:

362.0ms	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
113.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(/ a (* a c))
44.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

366.0ms	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
151.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(/ a (* a c))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5012
2	1660
1	470
0	197

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.7b

regimes794.0ms

Accuracy

91.3% (2.4b remaining)

Error of 7.7b against oracle of 5.4b and baseline of 32.5b

bsearch349.0ms

Steps

Iters	Range	Point
10	1.0955696400612189e+91	1.0202913897586463e+104	1.7205132563858266e+103
8	1.5743159256011981e-254	3.7434367033755896e-250	2.661523975777196e-253
9	-2.0190258033009663e+27	-4.429449841721669e+19	-3.234164035284793e+22

Iters

Range

Point

1.0955696400612189e+91

1.0202913897586463e+104

1.7205132563858266e+103

1.5743159256011981e-254

3.7434367033755896e-250

2.661523975777196e-253

-2.0190258033009663e+27

-4.429449841721669e+19

-3.234164035284793e+22

simplify18.0ms

Iterations

Iter	Nodes
done	42
1	42
0	34

end0.0ms

sample3.4s

Algorithm

intervals

Results

740.0ms	1081×	body	2560	valid
674.0ms	2917×	body	80	nan
629.0ms	5881×	body	80	valid
512.0ms	892×	body	1280	valid
152.0ms	437×	body	640	valid
73.0ms	113×	body	5120	valid
59.0ms	230×	body	320	valid
22.0ms	127×	body	160	valid