Details

sample66.0ms

Algorithm

intervals

Results

22.0ms	53×	body	1280	valid
12.0ms	137×	body	80	valid
12.0ms	32×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	11×	body	160	valid

simplify206.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
2.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
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 → 117

Calls

3 calls:

35.0ms	(/ (+ x 1) (- x 1))
16.0ms	(/ x (+ x 1))
61.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (+ x 1) (- x 1))
36.0ms	(/ x (+ x 1))
104.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	2001
3	2001
2	1062
1	399
0	180

prune480.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.1b	(* (/ x (- (* x x) 1)) (- x 1))
7.5b	(- (* (/ x (- (* x x) 1)) (- x 1)) (/ (+ x 1) (- x 1)))
13.9b	(/ x (- (* x x) 1))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
65×	`times-frac`
39×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-l`
13×	`associate-/r*` `add-cbrt-cube` `difference-of-sqr-1` `add-exp-log`
8×	`flip3--` `flip--` `distribute-lft-out`
7×	`associate-r` `associate-/l*`
6×	`pow1` `associate-/r/` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `frac-sub`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate--l+` `associate-*r/` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 176

Calls

4 calls:

33.0ms	(/ (+ x 1) (- x 1))
74.0ms	(* (/ x (- (* x x) 1)) (- x 1))
57.0ms	(- (* (/ x (- (* x x) 1)) (- x 1)) (/ (+ x 1) (- x 1)))
21.0ms	(/ x (- (* x x) 1))

series328.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1) (- x 1))
48.0ms	(* (/ x (- (* x x) 1)) (- x 1))
184.0ms	(- (* (/ x (- (* x x) 1)) (- x 1)) (/ (+ x 1) (- x 1)))
59.0ms	(/ x (- (* x x) 1))

simplify955.0ms

Counts

188 → 188

Iterations

Iter	Nodes
done	2001
2	2001
1	762
0	281

prune641.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3 x) (/ 1 (* x x)))
0.1b	(/ (/ 3 x) (* x x))
0.3b	(/ 1 (* x x))
8.3b	(+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

37×	`times-frac`
33×	`*-un-lft-identity`
27×	`add-exp-log`
21×	`add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/l*`
12×	`pow1`
11×	`add-log-exp`
10×	`div-exp`
8×	`cbrt-undiv` `div-inv` `distribute-lft-out`
6×	`pow-flip`
5×	`frac-add` `prod-exp`
4×	`sum-log` `insert-posit16`
3×	`flip3-+` `cbrt-unprod` `flip-+`
2×	`+-commutative` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `distribute-rgt-out` `1-exp`
1×	`pow2` `associate-+r+` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `inv-pow` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

24.0ms	(+ (/ 3 x) (/ 1 (* x x)))
18.0ms	(/ (/ 3 x) (* x x))
9.0ms	(/ 1 (* x x))
70.0ms	(+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (/ 3 x) (/ 1 (* x x)))
62.0ms	(/ (/ 3 x) (* x x))
18.0ms	(/ 1 (* x x))
44.0ms	(+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x))))

simplify915.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	2005
2	2005
1	606
0	201

prune387.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

8.3b	(+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x))))
21.4b	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))
21.4b	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))
21.4b	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
24×	`distribute-lft-out`
21×	`cbrt-prod`
16×	`frac-add`
15×	`cbrt-div`
9×	`add-log-exp`
8×	`flip3-+` `times-frac` `flip-+` `div-inv`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `distribute-rgt-out` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sum-log` `pow1/3`
1×	`+-commutative` `associate-+r+`

Counts

4 → 84

Calls

4 calls:

75.0ms	(+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x))))
47.0ms	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))
46.0ms	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))
52.0ms	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x))))
65.0ms	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))
66.0ms	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))
80.0ms	(cbrt (+ (/ (/ 3 x) (* x x)) (+ (/ 3 x) (/ 1 (* x x)))))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	2000
3	2000
2	1838
1	402
0	135

prune466.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.1b

bsearch108.0ms

Steps

Iters	Range		Point
10	0.001953933407705698	32640636.358721357	13311.743891071605
7	-16883.399250034305	-988.0224752747107	-12303.308137983877

simplify12.0ms

Iterations

Iter	Nodes
done	47
3	47
2	41
1	35
0	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

706.0ms	1700×	body	1280	valid
509.0ms	1280×	body	640	valid
349.0ms	4072×	body	80	valid
162.0ms	625×	body	320	valid
74.0ms	323×	body	160	valid