Details

sample85.0ms

Algorithm

intervals

Results

17.0ms	198×	body	80	valid
17.0ms	31×	body	2560	valid
12.0ms	28×	body	1280	valid
7.0ms	87×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize64.0ms

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))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

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:

87.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

107 → 107

Iterations

Iter	Nodes
done	5005
3	3743
2	1046
1	388
0	162

prune551.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.1b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite197.0ms

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:

47.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
40.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
253.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
268.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2110
1	614
0	241

prune654.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.7b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.1b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite189.0ms

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:

36.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
53.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
247.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
248.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
113.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1675
1	537
0	207

prune523.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize30.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* a (/ c (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))) a)
5.4b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
14.8b	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`log-prod` `exp-sum`
7×	`pow1` `sqrt-prod`
6×	`exp-prod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `insert-posit16`
3×	`associate-/r*` `times-frac` `flip3--` `log-pow` `flip--` `difference-of-squares`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-inv` `associate-/l` `distribute-lft-out--` `rem-exp-log` `associate-/l/`

Counts

4 → 81

Calls

4 calls:

41.0ms	(/ (* a (/ c (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))) a)
11.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
54.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (* a (/ c (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))) a)
70.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
83.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5016
2	1582
1	444
0	190

prune393.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

regimes488.0ms

Accuracy

87.8% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 33.2b

bsearch583.0ms

Steps

Iters	Range	Point
9	6.2301214455520334e+75	1.9082112581546424e+85	8.016779424032652e+82
9	-7.352001906045209e-176	-4.997881658352918e-184	-3.407079315314288e-176
8	-4.850690055273968e+74	-2.747294314478889e+71	-4.2887136042886476e+71

Iters

Range

Point

6.2301214455520334e+75

1.9082112581546424e+85

8.016779424032652e+82

-7.352001906045209e-176

-4.997881658352918e-184

-3.407079315314288e-176

-4.850690055273968e+74

-2.747294314478889e+71

-4.2887136042886476e+71

simplify16.0ms

Iterations

Iter	Nodes
done	46
1	46
0	38

end0.0ms

sample2.6s

Algorithm

intervals

Results

731.0ms	1060×	body	2560	valid
482.0ms	5839×	body	80	valid
417.0ms	889×	body	1280	valid
244.0ms	2843×	body	80	nan
166.0ms	114×	body	5120	valid
113.0ms	456×	body	640	valid
82.0ms	228×	body	320	valid
18.0ms	121×	body	160	valid