Details

sample145.0ms

Algorithm

intervals

Results

49.0ms	43×	body	2560	valid
17.0ms	164×	body	80	valid
16.0ms	32×	body	1280	valid
7.0ms	80×	body	80	nan
6.0ms	16×	body	640	valid
6.0ms	8×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	107
5	107
4	99
3	79
2	44
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
0.2b	(* (* 4.0 a) c)
1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

91.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
22.0ms	(* (* 4.0 a) c)
65.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
22.0ms	(* (* 4.0 a) c)
122.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1950
1	432
0	174

prune632.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.5b	(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.2b	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt c)
48.0ms	(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
7.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series884.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt c)
269.0ms	(cbrt c)
173.0ms	(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
149.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1002
1	245
0	104

prune482.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* 1 (- (sqrt (- (* b b) (* (* c 4.0) a))) b)) 2.0) a)
0.2b	(/ (* 1 (- (sqrt (- (* b b) (* (* c 4.0) a))) b)) 2.0)
1.5b	(- (sqrt (- (* b b) (* (* c 4.0) a))) b)
21.2b	(sqrt (- (* b b) (* (* c 4.0) a)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

65.0ms	(/ (/ (* 1 (- (sqrt (- (* b b) (* (* c 4.0) a))) b)) 2.0) a)
83.0ms	(/ (* 1 (- (sqrt (- (* b b) (* (* c 4.0) a))) b)) 2.0)
77.0ms	(- (sqrt (- (* b b) (* (* c 4.0) a))) b)
11.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (/ (* 1 (- (sqrt (- (* b b) (* (* c 4.0) a))) b)) 2.0) a)
146.0ms	(/ (* 1 (- (sqrt (- (* b b) (* (* c 4.0) a))) b)) 2.0)
138.0ms	(- (sqrt (- (* b b) (* (* c 4.0) a))) b)
117.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))

simplify2.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	3220
1	603
0	227

prune725.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize12.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

regimes509.0ms

Accuracy

87.7% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 39.5b

bsearch71.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.450829996567048e+138

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample3.3s

Algorithm

intervals

Results

615.0ms	1094×	body	2560	valid
594.0ms	5792×	body	80	valid
492.0ms	887×	body	1280	valid
472.0ms	243×	body	320	valid
238.0ms	2874×	body	80	nan
179.0ms	467×	body	640	valid
91.0ms	108×	body	5120	valid
16.0ms	117×	body	160	valid