Details

sample112.0ms

Algorithm

intervals

Results

29.0ms	198×	body	80	valid
22.0ms	37×	body	2560	valid
10.0ms	107×	body	80	nan
10.0ms	19×	body	1280	valid
6.0ms	13×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	160	valid

simplify140.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	140
7	140
6	138
5	135
4	132
3	113
2	62
1	29
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize28.0ms

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))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`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 → 157

Calls

4 calls:

114.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(- (* b b) (* 4.0 (* a c)))
127.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

169 → 169

Iterations

Iter	Nodes
done	5003
2	1814
1	601
0	241

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize29.0ms

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)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`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 → 157

Calls

4 calls:

88.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
67.0ms	(- (* b b) (* (* 4.0 a) c))
97.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
125.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

169 → 169

Iterations

Iter	Nodes
done	5002
2	1819
1	606
0	243

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize48.0ms

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)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 205

Calls

4 calls:

77.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
63.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

217 → 217

Iterations

Iter	Nodes
done	5001
2	2290
1	764
0	313

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- 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)))

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
291×	`add-sqr-sqrt`
290×	`*-un-lft-identity`
190×	`add-cube-cbrt`
87×	`add-exp-log`
61×	`prod-diff`
58×	`div-exp` `sqrt-prod`
50×	`distribute-lft-out--` `difference-of-squares`
46×	`distribute-rgt-neg-in`
37×	`div-inv`
27×	`associate-/r*`
25×	`add-cbrt-cube`
21×	`distribute-lft-neg-in`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `fma-neg` `flip--`
10×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 394

Calls

4 calls:

72.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
64.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

406 → 406

Iterations

Iter	Nodes
done	5001
2	3555
1	1479
0	524

prune2.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.9b

regimes565.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.9b

bsearch156.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	5913×	body	80	valid
620.0ms	1038×	body	2560	valid
441.0ms	906×	body	1280	valid
325.0ms	443×	body	640	valid
265.0ms	2911×	body	80	nan
101.0ms	241×	body	320	valid
71.0ms	110×	body	5120	valid
16.0ms	105×	body	160	valid