Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	60×	body	1280	valid
3.0ms	124×	body	80	valid
2.0ms	31×	body	640	valid
2.0ms	34×	body	320	valid
0.0ms	7×	body	160	valid

simplify110.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	76	13
9	97	13
10	127	13
11	137	13
12	141	13
13	143	13
done	143	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.4b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite77.0ms

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-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
57.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	176	1584
1	390	1503
2	1012	1427
3	2727	1414
done	5000	1414

prune207.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.2b	(/ 1.0 (* x x))
6.8b	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
53×	`times-frac`
37×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
16×	`add-log-exp`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube`
9×	`unpow3`
7×	`distribute-lft-out`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `distribute-rgt-out` `diff-log` `div-inv` `distribute-lft-out--` `sqr-pow`
3×	`cbrt-undiv` `sum-log` `frac-sub` `distribute-neg-frac`
2×	`distribute-rgt-neg-in` `frac-2neg` `flip3-+` `neg-log` `frac-add` `clear-num` `flip-+`
1×	`+-commutative` `associate--l-` `neg-sub0` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft1-in` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

40.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
3.0ms	(/ 1.0 (* x x))
125.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
35.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ 1.0 (* x x))
35.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify902.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (376.0ms)

Iter	Nodes	Cost
0	214	1988
1	535	1734
2	2052	1630
done	5000	1630

prune242.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (/ 1 (* x x)) 1) (/ 3.0 x))
0.2b	(/ 1.0 (* x x))
0.2b	(/ 1 (* x x))
6.8b	(- (- (/ 1.0 (* x x))) (* (+ (/ 1 (* x x)) 1) (/ 3.0 x)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cbrt-cube`
16×	`add-cube-cbrt` `times-frac`
14×	`pow1`
13×	`associate-r`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow-flip` `prod-exp` `associate-/l*`
5×	`cbrt-undiv` `associate-l` `frac-sub` `distribute-neg-frac`
4×	`frac-times` `flip3-+` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
2×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `distribute-lft-out` `unswap-sqr`
1×	`associate--l-` `pow2` `neg-sub0` `sub-neg` `flip3--` `pow-plus` `neg-log` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `inv-pow`

Counts

4 → 110

Calls

4 calls:

37.0ms	(* (+ (/ 1 (* x x)) 1) (/ 3.0 x))
3.0ms	(/ 1.0 (* x x))
4.0ms	(/ 1 (* x x))
24.0ms	(- (- (/ 1.0 (* x x))) (* (+ (/ 1 (* x x)) 1) (/ 3.0 x)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (+ (/ 1 (* x x)) 1) (/ 3.0 x))
25.0ms	(/ 1.0 (* x x))
17.0ms	(/ 1 (* x x))
35.0ms	(- (- (/ 1.0 (* x x))) (* (+ (/ 1 (* x x)) 1) (/ 3.0 x)))

simplify849.0ms

Counts

122 → 122

Iterations

Useful iterations: done (845.0ms)

Iter	Nodes	Cost
0	210	1807
1	563	1602
2	2072	1405
done	5001	1337

prune219.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
0.3b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
20.8b	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
42×	`cbrt-prod`
21×	`times-frac`
16×	`cbrt-div` `difference-of-squares`
14×	`add-cube-cbrt`
11×	`pow1` `distribute-lft-out--`
10×	`swap-sqr`
9×	`flip3--` `flip--`
8×	`pow1/3` `associate-r` `associate-l`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

2.0ms	(cbrt (- x 1.0))
2.0ms	(cbrt (- x 1.0))
19.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
137.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (- x 1.0))
99.0ms	(cbrt (- x 1.0))
126.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
176.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify645.0ms

Counts

124 → 124

Iterations

Useful iterations: done (641.0ms)

Iter	Nodes	Cost
0	238	2491
1	542	2339
2	1525	1940
done	5000	1917

prune264.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes36.0ms

Accuracy

100% (0.0b remaining)

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

bsearch80.0ms

Steps

Iters	Range		Point
11	4368.076441928604	1.2360357871274782e+23	9971.293289135534
8	-133622.27441454158	-436.72743869654124	-12787.016553276117

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	65
1	37	48
done	37	48

end0.0ms

sample523.0ms

Algorithm

intervals

Results

169.0ms	1668×	body	1280	valid
103.0ms	1254×	body	640	valid
96.0ms	4085×	body	80	valid
42.0ms	652×	body	320	valid
17.0ms	341×	body	160	valid