Details

sample63.0ms

Algorithm

intervals

Results

30.0ms	290×	body	80	valid
8.0ms	89×	body	80	nan

simplify191.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	616
1	39	616
2	79	616
3	143	616
4	179	616
5	189	616
6	193	616
done	193	616

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize141.0ms

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)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `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 → 151

Calls

4 calls:

40.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

163 → 163

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	179	85356
1	441	74970
2	1817	66601
done	5001	53231

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize228.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 83

Calls

4 calls:

31.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
142.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

95 → 95

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	178	48556
1	446	44508
2	1869	43715
done	5000	42860

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize186.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts

80 → 80

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	54	24556
1	147	21664
2	585	21504
3	3708	21504
done	5000	21404

prune748.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

localize200.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
3.9b	(/ (* a c) b)
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite510.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
10×	`fma-def`
8×	`add-log-exp`
6×	`times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `distribute-rgt-neg-in` `div-exp` `log1p-expm1-u` `associate-/l`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`clear-num` `sum-log` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `neg-log` `associate-+l-` `flip-+` `flip--`

Counts

4 → 90

Calls

4 calls:

33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
442.0ms	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
15.0ms	(/ (* a c) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
117.0ms	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
25.0ms	(/ (* a c) b)
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	179	26155
1	472	23892
2	2342	22852
done	5000	22827

prune879.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.8b

regimes432.0ms

Accuracy

93.9% (0.8b remaining)

Error of 7.0b against oracle of 6.2b and baseline of 19.9b

bsearch260.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	1.4828322806133274e+130
7	-5.856362438573669e+138	-1.280729871585891e+137	-5.791348048249166e+138

simplify28.0ms

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	45	1719
1	54	1719
done	54	1719

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	8727×	body	80	valid
388.0ms	2877×	body	80	nan