Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	55×	body	640	valid
4.0ms	135×	body	80	valid
3.0ms	22×	body	1280	valid
2.0ms	31×	body	320	valid
1.0ms	13×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	52	15
5	59	15
6	68	15
7	86	15
8	107	15
9	117	15
done	117	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

6.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ 1.0 (+ x 1.0))
44.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
210.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
27.0ms	(/ 1.0 (+ x 1.0))
50.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
233.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.6s

Counts

126 → 126

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	213	1832
1	499	1716
2	1288	1630
3	3776	1608
done	5000	1607

prune257.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
15.6b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-*l/`
36×	`flip3--` `flip--`
32×	`frac-add`
28×	`frac-times`
24×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
15×	`add-sqr-sqrt`
14×	`associate-*r/`
13×	`*-un-lft-identity`
11×	`pow1`
10×	`associate-r`
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`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

18.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
44.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
21.0ms	(* (* (+ x 1.0) x) (- x 1.0))
12.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series245.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
95.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
102.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify558.0ms

Counts

156 → 156

Iterations

Useful iterations: done (552.0ms)

Iter	Nodes	Cost
0	292	5330
1	1030	5037
done	5000	4991

prune475.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.9b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

10.0ms	(* (+ x 1.0) x)
22.0ms	(* (* (+ x 1.0) x) (- x 1.0))
18.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (+ x 1.0) x)
100.0ms	(* (* (+ x 1.0) x) (- x 1.0))
93.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify767.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (274.0ms)

Iter	Nodes	Cost
0	154	1283
1	426	1247
2	1778	1075
done	5001	1075

prune166.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
0.4b	(/ 2.0 (* (+ x 1.0) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
51×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/` `associate-/r/`
12×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`flip3-+` `flip-+` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-l`
3×	`associate-r` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 122

Calls

3 calls:

11.0ms	(* (+ x 1.0) x)
17.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
5.0ms	(/ 2.0 (* (+ x 1.0) x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (+ x 1.0) x)
91.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
35.0ms	(/ 2.0 (* (+ x 1.0) x))

simplify659.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	221	2097
1	561	1997
2	1783	1827
done	5000	1827

prune249.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
done	10	11

end0.0ms

sample610.0ms

Algorithm

intervals

Results

200.0ms	1886×	body	640	valid
126.0ms	4185×	body	80	valid
83.0ms	961×	body	320	valid
77.0ms	550×	body	1280	valid
23.0ms	420×	body	160	valid