Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	77×	body	640	valid
4.0ms	122×	body	80	valid
3.0ms	21×	body	1280	valid
2.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify74.0ms

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: 8.5b

localize8.0ms

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))
1.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite249.0ms

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:

7.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
38.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
194.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(/ 1.0 (- x 1.0))
48.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.7s

Counts

126 → 126

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	213	1832
1	499	1716
2	1288	1630
3	3777	1608
done	5001	1607

prune262.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
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))
16.6b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

10.0ms	(* (+ x 1.0) x)
39.0ms	(/ (+ (* (- (* 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))
14.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series418.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ x 1.0) x)
87.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
95.0ms	(* (* (+ x 1.0) x) (- x 1.0))
194.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify565.0ms

Counts

145 → 145

Iterations

Useful iterations: done (560.0ms)

Iter	Nodes	Cost
0	283	4761
1	1001	4516
done	5001	4484

prune429.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite52.0ms

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)
20.0ms	(* (* (+ x 1.0) x) (- x 1.0))
19.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* (+ x 1.0) x)
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
87.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify946.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (286.0ms)

Iter	Nodes	Cost
0	154	1283
1	426	1247
2	1778	1075
done	5000	1075

prune163.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize6.0ms

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))
0.2b	(/ 2.0 (* (+ x 1.0) x))

rewrite37.0ms

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:

13.0ms	(* (+ x 1.0) x)
14.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
5.0ms	(/ 2.0 (* (+ x 1.0) x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (+ x 1.0) x)
89.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
36.0ms	(/ 2.0 (* (+ x 1.0) x))

simplify793.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (287.0ms)

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

prune238.0ms

Pruning

3 alts after pruning (3 fresh and 0 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	9	11
done	9	11

end0.0ms

sample647.0ms

Algorithm

intervals

Results

218.0ms	1883×	body	640	valid
132.0ms	4149×	body	80	valid
85.0ms	568×	body	1280	valid
82.0ms	970×	body	320	valid
25.0ms	433×	body	160	valid