Details

sample64.0ms

Algorithm

intervals

Results

28.0ms	69×	body	640	valid
10.0ms	124×	body	80	valid
8.0ms	32×	body	320	valid
6.0ms	17×	body	1280	valid
2.0ms	14×	body	160	valid

simplify150.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize31.0ms

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))
2.9b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite242.0ms

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:

18.0ms	(/ 1 (- x 1))
17.0ms	(/ 1 (+ x 1))
40.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
163.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (- x 1))
16.0ms	(/ 1 (+ x 1))
38.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
123.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify13.9s

Counts

153 → 153

Iterations

Iter	Nodes
3	3950
2	1356
1	492
0	219

prune432.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
0.1b	(* (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
2.9b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
2.9b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

598×	`*-un-lft-identity`
192×	`distribute-lft-out`
179×	`sqrt-prod`
156×	`times-frac`
154×	`distribute-lft-out--`
95×	`div-inv`
72×	`swap-sqr`
65×	`sqrt-div`
45×	`frac-add`
26×	`add-sqr-sqrt`
25×	`frac-times`
20×	`pow1`
16×	`associate-r` `associate-l`
15×	`flip3-+` `flip3--` `frac-sub` `flip-+` `flip--`
14×	`add-log-exp`
13×	`add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-l/` `associate-r/` `pow-prod-up`
4×	`associate-+l+` `sum-log` `insert-posit16` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `sub-neg` `diff-log` `associate-+l-`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 256

Calls

4 calls:

214.0ms	(sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
911.0ms	(* (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
190.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
249.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
110.0ms	(* (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
136.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
130.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.9s

Counts

268 → 268

Iterations

Iter	Nodes
3	3910
2	1249
1	479
0	225

prune824.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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))
2.9b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite264.0ms

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:

13.0ms	(/ 1 (- x 1))
9.0ms	(/ 1 (+ x 1))
44.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
193.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))
33.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
133.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify12.9s

Counts

153 → 153

Iterations

Iter	Nodes
3	3950
2	1356
1	492
0	219

prune512.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1) x)
0.0b	(* (+ x 1) x)
0.1b	(* (* (+ x 1) x) (- x 1))
18.7b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

48×	`associate-*l/`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `frac-add`
15×	`flip3--` `flip--`
14×	`flip3-+` `flip-+`
13×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
12×	`frac-times`
9×	`associate-l` `add-cube-cbrt`
6×	`associate-*r/` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `associate-+l+` `sub-neg` `distribute-lft-in` `insert-posit16`
3×	`*-commutative`
2×	`distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `sum-log` `difference-of-sqr-1` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

29.0ms	(* (+ x 1) x)
28.0ms	(* (+ x 1) x)
61.0ms	(* (* (+ x 1) x) (- x 1))
39.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series262.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (+ x 1) x)
51.0ms	(* (+ x 1) x)
137.0ms	(* (* (+ x 1) x) (- x 1))
3.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify1.8s

Counts

123 → 123

Iterations

Iter	Nodes
2	3424
1	776
0	213

prune582.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	11
1	11
0	8

end0.0ms

sample2.5s

Algorithm

intervals

Results

913.0ms	1927×	body	640	valid
564.0ms	4108×	body	80	valid
442.0ms	564×	body	1280	valid
315.0ms	902×	body	320	valid
102.0ms	500×	body	160	valid