Details

sample54.0ms

Algorithm

intervals

Results

19.0ms	48×	body	640	valid
12.0ms	53×	body	1280	valid
6.0ms	118×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.2s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite151.0ms

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))
19.0ms	(/ (+ x 1.0) (- x 1.0))
119.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series318.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ x (+ x 1.0))
66.0ms	(/ (+ x 1.0) (- x 1.0))
190.0ms	(- (/ 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

prune532.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1.0 x) x)
0.1b	(* (* x x) x)
0.2b	(/ 3.0 (* (* x x) x))
5.6b	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ (/ 1.0 x) x)))

rewrite320.0ms

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:

9.0ms	(/ (/ 1.0 x) x)
22.0ms	(* (* x x) x)
15.0ms	(/ 3.0 (* (* x x) x))
269.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ (/ 1.0 x) x)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (/ 1.0 x) x)
65.0ms	(* (* x x) x)
51.0ms	(/ 3.0 (* (* x x) x))
51.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ (/ 1.0 x) x)))

simplify2.8s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
2	4960
1	758
0	267

prune623.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
7.6b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `frac-sub` `cbrt-unprod` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

9.0ms	(/ 1 (+ x 1.0))
33.0ms	(/ (+ x 1.0) (- x 1.0))
28.0ms	(* x (/ 1 (+ x 1.0)))
32.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (+ x 1.0))
52.0ms	(/ (+ x 1.0) (- x 1.0))
51.0ms	(* x (/ 1 (+ x 1.0)))
150.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	2572
1	529
0	210

prune562.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite33.0ms

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:

33.0ms

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

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

(+ (* 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

prune39.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch140.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	13113.526740685162
10	-17239113253358.373	-4.96108325192681e-05	-11444.735242389535

simplify5.0ms

Iterations

Iter	Nodes
done	36
1	36
0	25

end0.0ms

sample1.5s

Algorithm

intervals

Results

820.0ms	1740×	body	1280	valid
242.0ms	1239×	body	640	valid
160.0ms	4089×	body	80	valid
67.0ms	624×	body	320	valid
22.0ms	308×	body	160	valid