Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	36×	body	2560	valid
8.0ms	189×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	104×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

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--` `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 → 91

Calls

4 calls:

77.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
124.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
3	3629
2	1040
1	384
0	158

prune590.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.8b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.9b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
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×	`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 → 124

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
71.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b_2 b_2) (* a c))
261.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
302.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	2137
1	608
0	234

prune808.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.6b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.8b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
24×	`-un-lft-identity` `associate-r*`
22×	`times-frac`
18×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `flip3--` `associate-l*` `flip--` `distribute-lft-out--`
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 → 94

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
136.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
63.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series711.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b_2 b_2) (* a c))
324.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
237.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5004
2	1681
1	519
0	196

prune542.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.4b

localize45.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
27.0b	(cbrt (- (* b_2 b_2) (* a c)))
27.0b	(cbrt (- (* b_2 b_2) (* a c)))
27.0b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

108.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
141.0ms	(cbrt (- (* b_2 b_2) (* a c)))
133.0ms	(cbrt (- (* b_2 b_2) (* a c)))
141.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
4	4535
3	1473
2	657
1	342
0	182

prune562.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.4b

regimes430.0ms

Accuracy

90.1% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 31.7b

bsearch232.0ms

Steps

Iters	Range		Point
6	5.84949006905106e+100	6.027833473435204e+101	3.355858625783055e+101
10	4.8056470268910657e-293	9.518737492915906e-283	4.744536474227931e-289
11	-1.4585470499056154e+88	-9.653206849881042e+62	-7.741777288939024e+81

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample2.7s

Algorithm

intervals

Results

588.0ms	5821×	body	80	valid
501.0ms	1063×	body	2560	valid
450.0ms	116×	body	5120	valid
327.0ms	950×	body	1280	valid
208.0ms	2885×	body	80	nan
109.0ms	475×	body	640	valid
45.0ms	105×	body	160	valid
42.0ms	239×	body	320	valid