Details

sample94.0ms

Algorithm

intervals

Results

25.0ms	48×	body	640	valid
20.0ms	32×	body	320	valid
19.0ms	138×	body	80	valid
10.0ms	15×	body	1280	valid
6.0ms	23×	body	160	valid

simplify194.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	214
10	214
9	204
8	139
7	97
6	86
5	78
4	65
3	45
2	35
1	21
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(/ 1 (- x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
3.2b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

9.0ms	(/ 1 (+ x 1))
9.0ms	(/ 1 (- x 1))
31.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
164.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (+ x 1))
16.0ms	(/ 1 (- x 1))
33.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
115.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.7s

Counts

153 → 153

Iterations

Iter	Nodes
3	3644
2	1384
1	493
0	219

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(/ 1 (- x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
3.2b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

12.0ms	(/ 1 (+ x 1))
15.0ms	(/ 1 (- x 1))
58.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
168.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1 (+ x 1))
16.0ms	(/ 1 (- x 1))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
131.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.8s

Counts

153 → 153

Iterations

Iter	Nodes
3	3644
2	1384
1	493
0	219

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
0.0b	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
0.0b	(* (* (+ x 1) x) (- x 1))
16.3b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-*l/`
36×	`flip3--` `flip--`
32×	`frac-add`
28×	`frac-times`
24×	`flip3-+` `flip-+`
20×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
18×	`associate-/l/`
15×	`*-un-lft-identity`
14×	`associate-r` `associate-*r/`
11×	`pow1`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
4×	`associate-+l+` `associate-l` `pow-prod-down` `insert-posit16` `difference-of-squares`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`difference-of-sqr-1` `*-commutative` `distribute-lft-out--`
1×	`+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `div-inv` `unswap-sqr`

Counts

4 → 152

Calls

4 calls:

30.0ms	(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
124.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
57.0ms	(* (* (+ x 1) x) (- x 1))
52.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series187.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
65.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
96.0ms	(* (* (+ x 1) x) (- x 1))
2.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify2.7s

Counts

164 → 164

Iterations

Iter	Nodes
2	5165
1	1061
0	295

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* (+ x 1) x) (- x 1))
0.0b	(/ 2 (* (* (+ x 1) x) (- x 1)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

33.0ms	(* (* (+ x 1) x) (- x 1))
49.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

series252.0ms

Counts

2 → 6

Calls

2 calls:

150.0ms	(* (* (+ x 1) x) (- x 1))
102.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

simplify5.6s

Counts

73 → 73

Iterations

Iter	Nodes
3	6899
2	1636
1	414
0	139

prune517.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	13
1	13
0	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	1904×	body	640	valid
553.0ms	4074×	body	80	valid
401.0ms	586×	body	1280	valid
373.0ms	941×	body	320	valid
114.0ms	497×	body	160	valid