Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	61×	body	640	valid
5.0ms	134×	body	80	valid
4.0ms	33×	body	320	valid
3.0ms	16×	body	1280	valid
1.0ms	12×	body	160	valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	283
1	18	283
2	31	283
3	41	283
4	89	283
5	135	283
6	162	283
7	210	283
8	437	283
9	1188	283
10	4810	283
done	5001	283

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize36.0ms

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

rewrite465.0ms

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-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

9.0ms	(/ 1.0 (- x 1.0))
9.0ms	(/ 1.0 (+ x 1.0))
63.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
380.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- x 1.0))
26.0ms	(/ 1.0 (+ x 1.0))
72.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
295.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.4s

Counts

126 → 126

Iterations

Useful iterations: 2 (578.0ms)

Iter	Nodes	Cost
0	212	39541
1	515	33737
2	1951	32727
done	5001	32727

prune616.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
15.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
18×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
12×	`associate-*r/`
9×	`add-sqr-sqrt` `pow1` `*-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` `clear-num` `associate-/r` `sum-log` `frac-2neg` `diff-log` `associate-l` `-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 124

Calls

4 calls:

113.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
45.0ms	(* (* (+ x 1.0) x) (- x 1.0))
12.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
35.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series351.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
168.0ms	(* (* (+ x 1.0) x) (- x 1.0))
58.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
4.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify2.4s

Counts

136 → 136

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	279	81418
1	1014	68455
done	5001	67372

prune796.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
14.6b	(* (/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
15.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite518.0ms

Algorithm

rewrite-expression-head

Rules

45×	`associate-*l/`
25×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
16×	`flip3--` `associate-l` `frac-add` `flip--`
14×	`frac-times` `flip3-+` `flip-+`
11×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`-un-lft-identity` `associate-r/` `associate-/r/` `add-cube-cbrt` `add-log-exp`
6×	`pow-plus` `associate-r` `pow-prod-up`
4×	`associate-+l+` `pow-prod-down`
3×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `times-frac` `div-exp`
2×	`pow2` `pow-sqr` `*-commutative` `unswap-sqr`
1×	`+-commutative` `sum-log` `diff-log` `pow3` `div-inv`

Counts

4 → 114

Calls

4 calls:

21.0ms	(* (* x x) x)
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
453.0ms	(* (/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
32.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series351.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* x x) x)
55.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
256.0ms	(* (/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify1.9s

Counts

126 → 126

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	308	81187
1	1235	68888
done	5001	68127

prune766.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))
0.1b	(* (* x x) x)
0.2b	(/ 2.0 (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0))))
18.6b	(* (/ 2.0 (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-cbrt-cube` `add-exp-log`
30×	`pow1`
25×	`associate-*l/`
17×	`associate-l`
16×	`prod-exp` `associate-/r/` `cbrt-unprod`
14×	`add-sqr-sqrt` `frac-times`
11×	`*-un-lft-identity` `flip3-+` `add-cube-cbrt` `flip-+`
10×	`associate-r`
9×	`flip3--` `flip--`
8×	`associate-*r/`
7×	`pow-prod-down`
6×	`cbrt-undiv` `times-frac` `pow-plus` `div-exp` `pow-prod-up`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow3` `-commutative` `associate-/l`
2×	`pow2` `sub-neg` `pow-sqr` `div-inv` `unswap-sqr`
1×	`difference-cubes` `clear-num` `associate-/r*` `frac-2neg`

Counts

4 → 133

Calls

4 calls:

155.0ms	(* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))
20.0ms	(* (* x x) x)
64.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0))))
329.0ms	(* (/ 2.0 (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))
59.0ms	(* (* x x) x)
97.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0))))
278.0ms	(* (/ 2.0 (* (* (+ x 1.0) x) (- (* (* x x) x) (* (* 1.0 1.0) 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify1.4s

Counts

145 → 145

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	247	68656
1	947	57923
done	5001	56799

prune748.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

regimes75.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 16.1b

bsearch196.0ms

Steps

Iters	Range		Point
7	2.8683685891990685e+61	4.596657472632644e+62	2.908559783786779e+61
9	-6.2573470230411204e+22	-83422883652835.42	-1.5233605608570184e+22

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	33	1618
1	47	1618
done	47	1618

end0.0ms

sample2.0s

Algorithm

intervals

Results

478.0ms	441×	body	160	valid
473.0ms	1849×	body	640	valid
413.0ms	4139×	body	80	valid
294.0ms	979×	body	320	valid
167.0ms	594×	body	1280	valid