Details

sample48.0ms

Algorithm

intervals

Results

21.0ms	290×	body	80	valid
6.0ms	89×	body	80	nan

simplify214.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	179
6	179
5	175
4	163
3	136
2	78
1	38
0	20

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize190.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 63

Calls

4 calls:

34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
139.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify652.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1037
1	255
0	100

prune718.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize207.0ms

Local error

Found 4 expressions with local error:

6.8b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* c 4.0) a)))) (sqrt (cbrt (- (* b b) (* (* c 4.0) a))))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.3b	(cbrt (- (* b b) (* (* c 4.0) a)))
20.3b	(cbrt (- (* b b) (* (* c 4.0) a)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

Calls

4 calls:

11.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* c 4.0) a)))) (sqrt (cbrt (- (* b b) (* (* c 4.0) a))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))
10.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* c 4.0) a)))) (sqrt (cbrt (- (* b b) (* (* c 4.0) a))))))
128.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
123.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))
159.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))

simplify988.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1851
1	428
0	165

prune855.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize252.0ms

Local error

Found 4 expressions with local error:

19.5b	(sqrt (- (* b b) (* (* c 4.0) a)))
19.5b	(sqrt (- (* b b) (* (* c 4.0) a)))
19.5b	(sqrt (- (* b b) (* (* c 4.0) a)))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))
16.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))
7.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))
98.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))
86.0ms	(sqrt (- (* b b) (* (* c 4.0) a)))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	4513
2	766
1	204
0	79

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.8b

localize159.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b	(/ (- (- b) (- b (/ (* 2.0 a) (/ b c)))) (* 2.0 a))
5.3b	(/ (* 2.0 a) (/ b c))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
39×	`times-frac`
26×	`add-sqr-sqrt`
21×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
14×	`associate-/r*`
12×	`distribute-lft-out--`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`pow1` `distribute-rgt-neg-in`
4×	`div-inv`
3×	`prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`clear-num` `sum-log` `frac-2neg` `flip3--` `sqrt-div` `flip--` `distribute-lft-out` `difference-of-squares` `associate-/l/`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `neg-log` `associate-/r/` `associate-+l-` `flip-+`

Counts

4 → 110

Calls

4 calls:

36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
210.0ms	(/ (- (- b) (- b (/ (* 2.0 a) (/ b c)))) (* 2.0 a))
21.0ms	(/ (* 2.0 a) (/ b c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms	(/ (- (- b) (- b (/ (* 2.0 a) (/ b c)))) (* 2.0 a))
44.0ms	(/ (* 2.0 a) (/ b c))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
2	4098
1	677
0	245

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.7b

regimes490.0ms

Accuracy

93.3% (1.0b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 20.0b

bsearch253.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	1.4828322806133274e+130
7	-5.856362438573669e+138	-1.280729871585891e+137	-2.9539231443429135e+138

simplify17.0ms

Iterations

Iter	Nodes
done	60
1	60
0	48

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	8727×	body	80	valid
554.0ms	2877×	body	80	nan