Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	54×	body	640	valid
6.0ms	140×	body	80	valid
4.0ms	34×	body	320	valid
2.0ms	13×	body	1280	valid
1.0ms	15×	body	160	valid

simplify152.0ms

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	50	15
5	55	15
6	64	15
7	82	15
8	99	15
9	109	15
done	109	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.3b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite529.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
35×	`times-frac`
33×	`add-sqr-sqrt`
14×	`distribute-lft-out--`
13×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`distribute-lft-out`
8×	`difference-of-squares`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `flip3--` `frac-add` `flip--` `associate-/l*`
2×	`sub-neg` `associate-+l+` `diff-log` `sum-log` `associate-/r/` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

3 → 81

Calls

3 calls:

11.0ms	(/ 1.0 (- x 1.0))
107.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
406.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series398.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1.0 (- x 1.0))
55.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
307.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.3s

Counts

90 → 90

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	179	1458
1	423	1375
2	1148	1305
3	3429	1285
done	5002	1285

prune293.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

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))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
17.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

175.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
92.0ms	(* (* (+ x 1.0) x) (- x 1.0))
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
34.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series352.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
128.0ms	(* (* (+ x 1.0) x) (- x 1.0))
64.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify819.0ms

Counts

136 → 136

Iterations

Useful iterations: done (811.0ms)

Iter	Nodes	Cost
0	279	4788
1	993	4541
done	5000	4173

prune701.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))) (+ x 1.0))
0.1b	(* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
17.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

328.0ms	(* (/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))) (+ x 1.0))
80.0ms	(* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
37.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series261.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))) (+ x 1.0))
93.0ms	(* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))
60.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify886.0ms

Counts

130 → 130

Iterations

Useful iterations: done (870.0ms)

Iter	Nodes	Cost
0	307	5007
1	1155	4754
done	5000	4226

prune697.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ 2.0 (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0))))
0.1b	(* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))
1.9b	(* (/ 2.0 (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))) (+ x 1.0))

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

39.0ms	(* (+ x 1.0) x)
83.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0))))
81.0ms	(* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))
256.0ms	(* (/ 2.0 (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))) (+ x 1.0))

series362.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (+ x 1.0) x)
79.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0))))
64.0ms	(* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))
127.0ms	(* (/ 2.0 (* (* (+ x 1.0) x) (- (* x x) (* 1.0 1.0)))) (+ x 1.0))

simplify2.5s

Counts

139 → 139

Iterations

Useful iterations: 2 (943.0ms)

Iter	Nodes	Cost
0	224	2843
1	740	2689
2	3695	2221
done	5001	2221

prune411.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	17	23
done	17	23

end0.0ms

sample1.8s

Algorithm

intervals

Results

775.0ms	4203×	body	80	valid
493.0ms	1862×	body	640	valid
193.0ms	927×	body	320	valid
132.0ms	554×	body	1280	valid
43.0ms	455×	body	160	valid