Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
10.0ms	198×	body	80	valid
5.0ms	107×	body	80	nan
5.0ms	19×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify163.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	132
4	127
3	106
2	61
1	28
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite464.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

62.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
6.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
376.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms	(- (* b b) (* 4.0 (* a c)))
132.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts

89 → 89

Iterations

Iter	Nodes
done	5006
3	4673
2	1246
1	402
0	155

prune645.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

54.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
58.0ms	(- (* b b) (* 4.0 (* a c)))
143.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

137 → 137

Iterations

Iter	Nodes
done	5004
2	1822
1	572
0	226

prune618.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) a)
0.4b	(- (* b b) (* (* 4.0 c) a))
1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
20.7b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite131.0ms

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:

85.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) a)
12.0ms	(- (* b b) (* (* 4.0 c) a))
19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) a)
80.0ms	(- (* b b) (* (* 4.0 c) a))
99.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
104.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5002
3	4194
2	1140
1	392
0	160

prune677.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
0.4b	(- (* b b) (* (* 4.0 c) a))
1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
20.7b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

109.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
13.0ms	(- (* b b) (* (* 4.0 c) a))
20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
52.0ms	(- (* b b) (* (* 4.0 c) a))
113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
115.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1716
1	494
0	179

prune526.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes485.0ms

Accuracy

83.9% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 33.8b

bsearch160.0ms

Steps

Iters	Range		Point
6	4.2942163002471454e+116	2.920461936675284e+117	2.865381670376961e+117
9	-2.9209995635511727e-62	-5.172501488366762e-68	-2.5694949190681246e-64

simplify11.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample3.2s

Algorithm

intervals

Results

622.0ms	1038×	body	2560	valid
597.0ms	5913×	body	80	valid
543.0ms	443×	body	640	valid
402.0ms	906×	body	1280	valid
326.0ms	2911×	body	80	nan
127.0ms	241×	body	320	valid
89.0ms	110×	body	5120	valid
59.0ms	105×	body	160	valid