Details

sample132.0ms

Algorithm

intervals

Results

39.0ms	184×	body	80	valid
29.0ms	35×	body	2560	valid
17.0ms	28×	body	1280	valid
11.0ms	86×	body	80	nan
8.0ms	15×	body	640	valid
3.0ms	4×	body	5120	valid
3.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify138.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize39.0ms

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)))

rewrite93.0ms

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)
7.0ms	(- (* b b) (* (* 3 a) c))
56.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 3 a) c)
56.0ms	(- (* b b) (* (* 3 a) c))
122.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
3	3323
2	951
1	295
0	123

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.2b

localize35.0ms

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))))

rewrite90.0ms

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:

22.0ms	(* 3 (* a c))
9.0ms	(- (* b b) (* 3 (* a c)))
45.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 3 (* a c))
61.0ms	(- (* b b) (* 3 (* a c)))
106.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
115.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
3	2616
2	776
1	279
0	120

prune963.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize61.0ms

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))))

rewrite113.0ms

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:

36.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
47.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 3 (* a c))))
14.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
112.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
111.0ms	(sqrt (- (* b b) (* 3 (* a c))))
94.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify4.0s

Counts

76 → 76

Iterations

Iter	Nodes
4	6539
3	1981
2	592
1	190
0	81

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize65.0ms

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))))

rewrite32.0ms

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:

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

series406.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (- (* b b) (* 3 (* a c))))
93.0ms	(sqrt (- (* b b) (* 3 (* a c))))
117.0ms	(sqrt (- (* b b) (* 3 (* a c))))
106.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify2.6s

Counts

76 → 76

Iterations

Iter	Nodes
4	5071
3	1431
2	406
1	127
0	51

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

regimes461.0ms

Accuracy

84.8% (3.3b remaining)

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

bsearch152.0ms

Steps

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

simplify9.0ms

Iterations

Iter	Nodes
2	36
1	36
0	30

end0.0ms

sample3.8s

Algorithm

intervals

Results

994.0ms	1126×	body	2560	valid
855.0ms	915×	body	1280	valid
791.0ms	5836×	body	80	valid
447.0ms	2975×	body	80	nan
203.0ms	415×	body	640	valid
98.0ms	119×	body	5120	valid
76.0ms	239×	body	320	valid
25.0ms	114×	body	160	valid