Details

sample58.0ms

Algorithm

intervals

Results

23.0ms	67×	body	640	valid
9.0ms	135×	body	80	valid
7.0ms	31×	body	320	valid
4.0ms	12×	body	1280	valid
2.0ms	11×	body	160	valid

simplify507.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	198
9	198
8	170
7	103
6	83
5	72
4	60
3	41
2	31
1	18
0	10

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize122.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (- x 1.0))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite1.4s

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` `insert-posit16` `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 → 622

Calls

4 calls:

37.0ms	(/ 1.0 (+ x 1.0))
202.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
25.0ms	(/ 1.0 (- x 1.0))
896.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ x 1.0))
86.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
61.0ms	(/ 1.0 (- x 1.0))
323.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify6.4s

Counts

634 → 634

Iterations

Iter	Nodes
done	5004
2	3112
1	1193
0	505

prune5.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (- x 1.0))
2.6b	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

rewrite902.0ms

Algorithm

rewrite-expression-head

Rules

728×	`*-un-lft-identity`
710×	`times-frac`
526×	`add-sqr-sqrt`
500×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+r+`
94×	`distribute-lft-out`
66×	`div-inv`
60×	`associate-/r/`
29×	`flip3-+` `flip-+`
21×	`fma-def`
18×	`fma-neg`
17×	`distribute-lft-out--`
11×	`add-log-exp` `difference-of-squares`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`frac-add`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+r-`

Counts

4 → 633

Calls

4 calls:

44.0ms	(/ 1.0 (+ x 1.0))
187.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
22.0ms	(/ 1.0 (- x 1.0))
431.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1.0 (+ x 1.0))
76.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
39.0ms	(/ 1.0 (- x 1.0))
408.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

simplify7.3s

Counts

645 → 645

Iterations

Iter	Nodes
done	5000
2	3976
1	1560
0	686

prune5.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize148.0ms

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	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
16.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite644.0ms

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` `insert-posit16` `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 → 175

Calls

4 calls:

309.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
34.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
162.0ms	(* (* (+ x 1.0) x) (- x 1.0))
107.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series408.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
78.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
154.0ms	(* (* (+ x 1.0) x) (- x 1.0))
4.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify3.3s

Counts

187 → 187

Iterations

Iter	Nodes
done	5001
1	1250
0	356

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 3 expressions with local error:

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

rewrite329.0ms

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` `insert-posit16` `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 → 111

Calls

3 calls:

88.0ms	(* (+ x 1.0) x)
126.0ms	(* (* (+ x 1.0) x) (- x 1.0))
95.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series409.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (+ x 1.0) x)
175.0ms	(* (* (+ x 1.0) x) (- x 1.0))
166.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify4.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1911
1	615
0	209

prune853.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample2.5s

Algorithm

intervals

Results

834.0ms	4086×	body	80	valid
813.0ms	1908×	body	640	valid
334.0ms	594×	body	1280	valid
237.0ms	972×	body	320	valid
70.0ms	441×	body	160	valid