Details

sample50.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
9.0ms	41×	body	640	valid
7.0ms	124×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.6s

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ 1.0 x))
0.0b	(/ (+ 1.0 x) (- x 1.0))
3.6b	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- 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 (+ 1.0 x))
33.0ms	(/ (+ 1.0 x) (- x 1.0))
106.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ x (+ 1.0 x))
69.0ms	(/ (+ 1.0 x) (- x 1.0))
181.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

simplify807.0ms

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1826
1	417
0	178

prune433.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x))))
0.1b	(/ 3.0 (pow x 3))
0.5b	(/ 1.0 (* x x))
7.3b	(+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

41×	`times-frac`
40×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`cube-mult` `div-exp` `frac-add` `distribute-lft-out`
4×	`pow1` `sum-log` `unpow3` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+`
2×	`+-commutative` `clear-num` `frac-2neg` `div-inv`
1×	`pow-to-exp` `associate-+r+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

176.0ms	(+ (/ 3.0 x) (+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x))))
13.0ms	(/ 3.0 (pow x 3))
9.0ms	(/ 1.0 (* x x))
53.0ms	(+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (/ 3.0 x) (+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x))))
53.0ms	(/ 3.0 (pow x 3))
44.0ms	(/ 1.0 (* x x))
112.0ms	(+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x)))

simplify2.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	4184
1	551
0	194

prune440.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
24.2b	(- (/ (* (cbrt x) (cbrt x)) (/ (+ 1.0 x) (cbrt x))) (/ (+ 1.0 x) (- x 1.0)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
14×	`times-frac`
11×	`cbrt-prod`
9×	`*-un-lft-identity`
8×	`difference-of-squares`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
135.0ms	(- (/ (* (cbrt x) (cbrt x)) (/ (+ 1.0 x) (cbrt x))) (/ (+ 1.0 x) (- x 1.0)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt x)
241.0ms	(cbrt x)
253.0ms	(cbrt x)
199.0ms	(- (/ (* (cbrt x) (cbrt x)) (/ (+ 1.0 x) (cbrt x))) (/ (+ 1.0 x) (- x 1.0)))

simplify1.8s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	4588
2	822
1	238
0	100

prune274.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ 1.0 x))
0.0b	(- (/ x (+ 1.0 x)) (- (+ (* 2.0 (+ x (* x x))) 1.0)))
0.0b	(+ x (* x x))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt` `add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-/r*` `distribute-lft-out`
3×	`pow1` `flip3-+` `diff-log` `flip-+` `associate-/l*`
2×	`sum-log` `neg-log` `associate-/r/` `frac-sub` `distribute-neg-frac` `distribute-lft-out--` `difference-of-squares`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `distribute-neg-in` `clear-num` `sub-neg` `distribute-rgt-neg-in` `frac-2neg` `distribute-rgt-out` `flip3--` `div-exp` `distribute-rgt1-in` `div-inv` `flip--` `associate--r+` `associate--r-`

Counts

3 → 68

Calls

3 calls:

11.0ms	(/ x (+ 1.0 x))
129.0ms	(- (/ x (+ 1.0 x)) (- (+ (* 2.0 (+ x (* x x))) 1.0)))
7.0ms	(+ x (* x x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ x (+ 1.0 x))
66.0ms	(- (/ x (+ 1.0 x)) (- (+ (* 2.0 (+ x (* x x))) 1.0)))
66.0ms	(+ x (* x x))

simplify1.3s

Counts

77 → 77

Iterations

Iter	Nodes
done	5002
2	2738
1	455
0	160

prune361.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

100% (0.0b remaining)

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

bsearch134.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	7229.990696850788
11	-14746478108.679678	-8.433739504313006e-14	-7087.2986999786435

simplify7.0ms

Iterations

Iter	Nodes
done	45
3	45
2	42
1	35
0	26

end0.0ms

sample1.5s

Algorithm

intervals

Results

528.0ms	4092×	body	80	valid
405.0ms	1694×	body	1280	valid
253.0ms	1237×	body	640	valid
103.0ms	638×	body	320	valid
60.0ms	339×	body	160	valid