Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	53×	body	1280	valid
5.0ms	39×	body	640	valid
5.0ms	129×	body	80	valid
3.0ms	27×	body	320	valid
0.0ms	8×	body	160	valid

simplify263.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite128.0ms

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))
28.0ms	(/ (+ x 1.0) (- x 1.0))
88.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series291.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ x (+ x 1.0))
63.0ms	(/ (+ x 1.0) (- x 1.0))
168.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1284
1	408
0	176

prune472.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.4b	(/ 1.0 (* x x))
0.7b	(/ (- 3.0) (* x (* x x)))
8.2b	(- (/ (- 3.0) (* x (* x x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

23.0ms	(* x (* x x))
11.0ms	(/ 1.0 (* x x))
27.0ms	(/ (- 3.0) (* x (* x x)))
170.0ms	(- (/ (- 3.0) (* x (* x x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* x (* x x))
50.0ms	(/ 1.0 (* x x))
73.0ms	(/ (- 3.0) (* x (* x x)))
62.0ms	(- (/ (- 3.0) (* x (* x x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

simplify1.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	2025
1	507
0	192

prune441.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

21.0ms

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

series104.0ms

Counts

1 → 3

Calls

1 calls:

103.0ms

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

simplify2.7s

Counts

25 → 25

Iterations

Iter	Nodes
done	5014
3	2947
2	569
1	158
0	50

prune101.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 3.0 (* x x)) (* x 1.0))
0.1b	(* x (* x x))
0.2b	(* 3.0 (* x x))
21.2b	(/ (- (- 3.0) (+ (* 3.0 (* x x)) (* x 1.0))) (* x (* x x)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

25.0ms	(+ (* 3.0 (* x x)) (* x 1.0))
25.0ms	(* x (* x x))
26.0ms	(* 3.0 (* x x))
168.0ms	(/ (- (- 3.0) (+ (* 3.0 (* x x)) (* x 1.0))) (* x (* x x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (* 3.0 (* x x)) (* x 1.0))
47.0ms	(* x (* x x))
48.0ms	(* 3.0 (* x x))
91.0ms	(/ (- (- 3.0) (+ (* 3.0 (* x x)) (* x 1.0))) (* x (* x x)))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5007
2	1885
1	394
0	140

prune337.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 32.3b

bsearch113.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	1.021370211112824
10	-84463.33967257517	-3.2432757514909933e-09	-0.9983730585657322

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

749.0ms	1644×	body	1280	valid
246.0ms	1270×	body	640	valid
201.0ms	4151×	body	80	valid
150.0ms	638×	body	320	valid
63.0ms	297×	body	160	valid