Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	51×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	124×	body	80	valid
3.0ms	30×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4085
11	1745
10	535
9	183
8	79
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
20.0ms	(/ (+ x 1.0) (- x 1.0))
107.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series332.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ x (+ x 1.0))
62.0ms	(/ (+ x 1.0) (- x 1.0))
209.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1794
1	408
0	176

prune435.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ 3.0 (* (* x x) x))
0.1b	(/ (/ 1.0 x) x)
5.8b	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ (/ 1.0 x) x)))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
59×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
23×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
14×	`add-log-exp`
6×	`cbrt-undiv` `pow-plus` `div-exp` `prod-exp` `pow-prod-up` `cbrt-unprod` `div-inv`
4×	`associate-/r*` `diff-log` `distribute-lft-out--`
3×	`associate-r` `pow-prod-down` `frac-sub` `distribute-neg-frac`
2×	`pow2` `clear-num` `sum-log` `distribute-rgt-neg-in` `frac-2neg` `neg-log` `pow-sqr` `distribute-lft-out`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3-+` `flip3--` `associate-l` `pow3` `frac-add` `*-commutative` `flip-+` `flip--` `associate--r+` `difference-of-squares` `unswap-sqr` `associate-/l/`

Counts

4 → 146

Calls

4 calls:

16.0ms	(* (* x x) x)
22.0ms	(/ 3.0 (* (* x x) x))
11.0ms	(/ (/ 1.0 x) x)
267.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ (/ 1.0 x) x)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* x x) x)
52.0ms	(/ 3.0 (* (* x x) x))
43.0ms	(/ (/ 1.0 x) x)
52.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ (/ 1.0 x) x)))

simplify2.6s

Counts

158 → 158

Iterations

Iter	Nodes
done	5002
2	4773
1	740
0	267

prune460.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* (/ x (* (+ x 1.0) (- x 1.0))) (- x 1.0))
7.0b	(- (* (/ x (* (+ x 1.0) (- x 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
15.0b	(/ x (* (+ x 1.0) (- x 1.0)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`times-frac`
20×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
18×	`associate-/r/`
15×	`associate-l`
12×	`frac-times` `flip3--` `flip--`
8×	`associate-*r/`
7×	`flip3-+` `flip-+` `associate-/l*`
6×	`pow1` `associate-/r` `associate-l/` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `sub-neg` `div-exp` `associate-r` `prod-exp` `frac-sub` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

22.0ms	(/ (+ x 1.0) (- x 1.0))
62.0ms	(* (/ x (* (+ x 1.0) (- x 1.0))) (- x 1.0))
62.0ms	(- (* (/ x (* (+ x 1.0) (- x 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
25.0ms	(/ x (* (+ x 1.0) (- x 1.0)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (+ x 1.0) (- x 1.0))
44.0ms	(* (/ x (* (+ x 1.0) (- x 1.0))) (- x 1.0))
173.0ms	(- (* (/ x (* (+ x 1.0) (- x 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
104.0ms	(/ x (* (+ x 1.0) (- x 1.0)))

simplify2.4s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
2	4878
1	730
0	256

prune593.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (* x 3.0) (+ (* 1.0 (* x x)) 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
3×	`sum-log`
1×	`add-sqr-sqrt` `pow1` `+-commutative` `associate-+r+` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+`

Counts

1 → 13

Calls

1 calls:

45.0ms

(+ (* x 3.0) (+ (* 1.0 (* x x)) 1.0))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(+ (* x 3.0) (+ (* 1.0 (* x x)) 1.0))

simplify2.4s

Counts

16 → 16

Iterations

Iter	Nodes
done	5000
3	4171
2	607
1	139
0	40

prune48.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.8b

bsearch135.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	12586.319453988886
11	-14746478108.679678	-8.433739504313006e-14	-9689.783168792597

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample1.4s

Algorithm

intervals

Results

716.0ms	1694×	body	1280	valid
227.0ms	1237×	body	640	valid
153.0ms	4092×	body	80	valid
63.0ms	638×	body	320	valid
27.0ms	339×	body	160	valid