Details

sample140.0ms

Algorithm

intervals

Results

34.0ms	35×	body	2560	valid
29.0ms	184×	body	80	valid
22.0ms	28×	body	1280	valid
13.0ms	86×	body	80	nan
10.0ms	15×	body	640	valid
5.0ms	4×	body	5120	valid
4.0ms	8×	body	320	valid
2.0ms	5×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
0.6b	(- (* b b) (* (* 3 a) c))
1.7b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
24.6b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (* 3 a) c)
11.0ms	(- (* b b) (* (* 3 a) c))
52.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 3 a) c)
61.0ms	(- (* b b) (* (* 3 a) c))
92.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
83.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	2002
3	2002
2	910
1	297
0	123

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (* a c))
0.6b	(- (* b b) (* 3 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
24.6b	(sqrt (- (* b b) (* 3 (* a c))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

24.0ms	(* 3 (* a c))
17.0ms	(- (* b b) (* 3 (* a c)))
40.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
12.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 3 (* a c))
53.0ms	(- (* b b) (* 3 (* a c)))
139.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
121.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify890.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2007
3	2007
2	780
1	281
0	120

prune672.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize37.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
1.7b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
24.6b	(sqrt (- (* b b) (* 3 (* a c))))
24.6b	(sqrt (- (* b b) (* 3 (* a c))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

37.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
42.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
9.0ms	(sqrt (- (* b b) (* 3 (* a c))))
8.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
96.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
90.0ms	(sqrt (- (* b b) (* 3 (* a c))))
82.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify842.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2024
3	2024
2	570
1	192
0	81

prune980.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize55.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (- (* b b) (* 3 (* a c))))
24.6b	(sqrt (- (* b b) (* 3 (* a c))))
24.6b	(sqrt (- (* b b) (* 3 (* a c))))
24.6b	(sqrt (- (* b b) (* 3 (* a c))))

rewrite37.0ms

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` `insert-posit16` `flip--` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* 3 (* a c))))
9.0ms	(sqrt (- (* b b) (* 3 (* a c))))
12.0ms	(sqrt (- (* b b) (* 3 (* a c))))
7.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (- (* b b) (* 3 (* a c))))
79.0ms	(sqrt (- (* b b) (* 3 (* a c))))
100.0ms	(sqrt (- (* b b) (* 3 (* a c))))
92.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify1.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	2008
4	2008
3	1765
2	399
1	129
0	51

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

regimes517.0ms

Accuracy

84.8% (3.3b remaining)

Error of 15.4b against oracle of 12.1b and baseline of 33.7b

bsearch180.0ms

Steps

Iters	Range		Point
8	2.5972983117194536e-74	3.3630379012102994e-71	3.32629031803127e-71
6	-2.5114071469885315e+112	-1.8217288728729631e+111	-1.277637730923319e+112

simplify12.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.1s	5836×	body	80	valid
937.0ms	1126×	body	2560	valid
646.0ms	915×	body	1280	valid
637.0ms	415×	body	640	valid
556.0ms	239×	body	320	valid
348.0ms	2975×	body	80	nan
162.0ms	119×	body	5120	valid
28.0ms	114×	body	160	valid