Details

sample98.0ms

Algorithm

intervals

Results

50.0ms	278×	body	80	valid
11.0ms	95×	body	80	nan

simplify212.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	20	38
1	39	38
2	79	37
3	143	37
4	179	37
5	189	37
6	193	37
done	193	37

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize155.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite148.0ms

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×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

44.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

163 → 163

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	179	6238
1	441	4232
2	1817	3344
done	5000	2696

prune767.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize133.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

153 → 153

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	164	6178
1	397	4161
2	1582	3305
done	5000	2665

prune854.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.4b

localize174.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.7b	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `fma-udef`

Counts

4 → 134

Calls

4 calls:

67.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
219.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

146 → 146

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	176	6153
1	417	4178
2	1624	3295
done	5001	2573

prune765.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.4b

localize178.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
23.0b	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
23.0b	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
2.0ms	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
3.0ms	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
31.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
125.0ms	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
130.0ms	(sqrt (fma c (- (* 4.0 a)) (pow b 2)))
129.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

74 → 74

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	71	934
1	173	821
2	612	776
3	3538	776
done	5000	775

prune593.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.4b

regimes223.0ms

Accuracy

85.3% (1.9b remaining)

Error of 9.4b against oracle of 7.5b and baseline of 20.2b

bsearch303.0ms

Steps

Iters	Range		Point
10	1.3113650301339767e-12	0.01077406869848718	0.010648423176581222
6	-1.1000082512799256e+103	-1.2658565361216573e+102	-6.402360759158877e+102

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	122
1	47	122
done	47	122

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	8705×	body	80	valid
792.0ms	3037×	body	80	nan