Details

sample81.0ms

Algorithm

intervals

Results

15.0ms	196×	body	80	valid
10.0ms	31×	body	1280	valid
10.0ms	16×	body	640	valid
10.0ms	27×	body	2560	valid
6.0ms	92×	body	80	nan
2.0ms	5×	body	5120	valid
1.0ms	3×	body	320	valid
1.0ms	4×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	102	16
5	111	16
done	111	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

125.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
18.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
126.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(- (* b b) (* 4.0 (* a c)))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify856.0ms

Counts

84 → 84

Iterations

Useful iterations: done (852.0ms)

Iter	Nodes	Cost
0	152	1592
1	403	1496
2	1596	1332
done	5001	1326

prune364.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

91.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
89.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
116.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
83.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

130 → 130

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	218	3137
1	566	2809
2	2636	2613
done	5000	2611

prune479.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

15.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(- (* b b) (* 4.0 (* a c)))
93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
99.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.6s

Counts

66 → 66

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	60	1010
1	160	930
2	631	834
3	3660	834
done	5000	834

prune314.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
5.6b	(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)) (/ b (* 2.0 a)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

21.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
11.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)) (/ b (* 2.0 a)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
54.0ms	(- (* b b) (* 4.0 (* a c)))
123.0ms	(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)) (/ b (* 2.0 a)))
83.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	161	1718
1	422	1572
2	1613	1436
done	5001	1432

prune269.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes404.0ms

Accuracy

85.2% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.5b

bsearch120.0ms

Steps

Iters	Range		Point
5	6.945766558749631e-52	1.7836275468166073e-51	8.70366778308292e-52
8	-1.5489453231745737e+155	-2.021963087226922e+151	-2.2976245343188767e+152

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	42
1	32	42
done	32	42

end0.0ms

sample3.5s

Algorithm

intervals

Results

814.0ms	1069×	body	2560	valid
719.0ms	5754×	body	80	valid
705.0ms	2912×	body	80	nan
428.0ms	917×	body	1280	valid
149.0ms	488×	body	640	valid
64.0ms	109×	body	5120	valid
58.0ms	246×	body	320	valid
13.0ms	91×	body	160	valid