Details

sample86.0ms

Algorithm

intervals

Results

15.0ms	32×	body	2560	valid
14.0ms	172×	body	80	valid
13.0ms	34×	body	1280	valid
8.0ms	105×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	9×	body	160	valid
1.0ms	5×	body	320	valid

simplify74.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
2.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite248.0ms

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

Counts

4 → 91

Calls

4 calls:

144.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(- (* b_2 b_2) (* a c))
136.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
118.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.6s

Counts

103 → 103

Iterations

Iter	Nodes
done	5002
3	3710
2	1027
1	378
0	156

prune837.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
2.0b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

17.0ms	(- (* b_2 b_2) (* a c))
176.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
109.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series854.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b_2 b_2) (* a c))
313.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
359.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.4s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	2134
1	608
0	234

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.3b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.0b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
221.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
74.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
28.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series826.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b_2 b_2) (* a c))
366.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
281.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5003
2	1680
1	519
0	196

prune905.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.3b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.0b	(* (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ 1 a))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
41×	`add-sqr-sqrt`
37×	`associate-r`
30×	`add-cbrt-cube`
29×	`*-un-lft-identity`
28×	`times-frac`
23×	`add-cube-cbrt`
22×	`prod-exp`
12×	`pow1` `cbrt-unprod`
11×	`div-exp`
6×	`cbrt-undiv` `sqrt-prod` `add-log-exp` `difference-of-squares`
4×	`associate-r/` `associate-l*` `pow-prod-down`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `distribute-lft-out--`
2×	`sqrt-div` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*l/` `un-div-inv`

Counts

4 → 116

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
219.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
270.0ms	(* (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ 1 a))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series805.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* b_2 b_2) (* a c))
342.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
285.0ms	(* (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ 1 a))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2127
1	651
0	233

prune957.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

regimes455.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 32.5b

bsearch315.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	5.748502676649783e+143
10	-7.365577167502996e-116	-4.228998172927506e-127	-4.296272708131499e-127
9	-4.447404991929899e+78	-8.380652639018829e+71	-5.999462245480892e+73

simplify15.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample3.6s

Algorithm

intervals

Results

852.0ms	2820×	body	80	nan
732.0ms	1055×	body	2560	valid
632.0ms	5836×	body	80	valid
454.0ms	909×	body	1280	valid
239.0ms	452×	body	640	valid
68.0ms	126×	body	160	valid
66.0ms	105×	body	5120	valid
52.0ms	227×	body	320	valid