Details

sample72.0ms

Algorithm

intervals

Results

33.0ms	282×	body	80	valid
9.0ms	107×	body	80	nan

simplify172.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
7	168
6	166
5	160
4	151
3	127
2	74
1	38
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize143.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite100.0ms

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:

36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
3	3019
2	764
1	246
0	100

prune694.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize171.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `distribute-rgt-neg-in` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 60

Calls

4 calls:

19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2701
2	687
1	216
0	83

prune719.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize175.0ms

Local error

Found 4 expressions with local error:

9.4b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite325.0ms

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:

10.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
304.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
112.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5003
3	4737
2	1161
1	366
0	149

prune819.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize245.0ms

Local error

Found 4 expressions with local error:

21.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
134.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
145.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
179.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	1648
2	460
1	153
0	65

prune687.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

regimes455.0ms

Accuracy

92.1% (1.0b remaining)

Error of 7.7b against oracle of 6.7b and baseline of 19.8b

bsearch257.0ms

Steps

Iters	Range		Point
6	4.2942163002471454e+116	2.920461936675284e+117	2.4732339682798126e+117
10	-4.109726801604347e+134	-3.694504963276933e+119	-1.2486341378981079e+132

simplify23.0ms

Iterations

Iter	Nodes
done	57
1	57
0	48

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	8756×	body	80	valid
269.0ms	2911×	body	80	nan