Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	61×	body	640	valid
8.0ms	134×	body	80	valid
5.0ms	33×	body	320	valid
4.0ms	16×	body	1280	valid
1.0ms	12×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize35.0ms

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)))

rewrite641.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

18.0ms	(/ 1.0 (- x 1.0))
18.0ms	(/ 1.0 (+ x 1.0))
92.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
446.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
37.0ms	(/ 1.0 (+ x 1.0))
61.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
276.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.4s

Counts

630 → 630

Iterations

Iter	Nodes
done	5000
2	4187
1	1192
0	501

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

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))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
37×	`prod-diff`
33×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`frac-add`
31×	`flip3--` `add-cube-cbrt` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
18×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
12×	`associate-*r/`
9×	`pow1`
8×	`associate-/r/` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `fma-def` `frac-2neg` `fma-neg` `diff-log` `associate-l` `-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 171

Calls

4 calls:

84.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
39.0ms	(* (* (+ x 1.0) x) (- x 1.0))
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
31.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series300.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
124.0ms	(* (* (+ x 1.0) x) (- x 1.0))
53.0ms	(- (* 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))

simplify1.6s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
1	1255
0	352

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff` `associate-*l/`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
8×	`frac-times` `associate-r` `associate-/r/`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`flip3--` `flip--`
5×	`associate-l`
4×	`pow-prod-down` `associate-*r/`
3×	`expm1-log1p-u` `cbrt-undiv` `times-frac` `div-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`sub-neg` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 108

Calls

3 calls:

18.0ms	(* (+ x 1.0) x)
67.0ms	(* (* (+ x 1.0) x) (- x 1.0))
58.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series298.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (+ x 1.0) x)
116.0ms	(* (* (+ x 1.0) x) (- x 1.0))
127.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify2.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	4484
1	617
0	206

prune698.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
0.3b	(/ 2.0 (* (+ x 1.0) x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
51×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
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×	`expm1-log1p-u` `associate-r` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out` `unswap-sqr` `associate-/l/`

Counts

3 → 128

Calls

3 calls:

33.0ms	(* (+ x 1.0) x)
44.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
23.0ms	(/ 2.0 (* (+ x 1.0) x))

series228.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* (+ x 1.0) x)
126.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
46.0ms	(/ 2.0 (* (+ x 1.0) x))

simplify2.6s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	3329
1	609
0	227

prune616.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

637.0ms	1849×	body	640	valid
294.0ms	979×	body	320	valid
260.0ms	4139×	body	80	valid
175.0ms	594×	body	1280	valid
100.0ms	441×	body	160	valid