Details

sample60.0ms

Algorithm

intervals

Results

19.0ms	65×	body	640	valid
10.0ms	27×	body	1280	valid
9.0ms	122×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	15×	body	160	valid

simplify133.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize18.0ms

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

rewrite738.0ms

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-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

11.0ms	(/ 1.0 (- x 1.0))
92.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms	(/ 1.0 (+ x 1.0))
564.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1.0 (- x 1.0))
57.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
34.0ms	(/ 1.0 (+ x 1.0))
323.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.9s

Counts

630 → 630

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	502	19834
1	1149	17345
2	2802	12902
done	5000	10138

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 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))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
33.7b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

77.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
18.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
79.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series943.0ms

Counts

4 → 12

Calls

4 calls:

440.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
54.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
163.0ms	(* (* (+ x 1.0) x) (- x 1.0))
285.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify2.5s

Counts

123 → 123

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	227	3140
1	618	2926
2	2311	2478
done	5000	2453

prune385.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.4b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
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×	`associate-*r/` `pow-prod-down`
3×	`cbrt-undiv` `expm1-log1p-u` `times-frac` `div-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`sub-neg` `*-commutative`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 108

Calls

3 calls:

29.0ms	(* (+ x 1.0) x)
51.0ms	(* (* (+ x 1.0) x) (- x 1.0))
47.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series293.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (+ x 1.0) x)
117.0ms	(* (* (+ x 1.0) x) (- x 1.0))
117.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify2.0s

Counts

117 → 117

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	206	1975
1	542	1770
2	1995	1511
done	5000	1486

prune234.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ 2.0 (- x 1.0))
0.1b	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
0.3b	(/ 1 (* (+ x 1.0) x))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
50×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-cbrt-cube`
29×	`add-cube-cbrt`
24×	`associate-r` `prod-exp`
20×	`div-exp`
13×	`associate-l`
11×	`pow1`
10×	`cbrt-undiv` `cbrt-unprod`
8×	`associate-/r/`
7×	`associate-*l/` `distribute-lft-out--` `difference-of-squares`
6×	`rec-exp` `1-exp` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `unswap-sqr`
2×	`flip3--` `pow-flip` `frac-2neg` `clear-num` `*-commutative` `flip--`
1×	`frac-times` `associate-*r/` `distribute-lft-out` `inv-pow`

Counts

4 → 160

Calls

4 calls:

21.0ms	(* (+ x 1.0) x)
12.0ms	(/ 2.0 (- x 1.0))
150.0ms	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
21.0ms	(/ 1 (* (+ x 1.0) x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ x 1.0) x)
32.0ms	(/ 2.0 (- x 1.0))
126.0ms	(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
49.0ms	(/ 1 (* (+ x 1.0) x))

simplify1.5s

Counts

172 → 172

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	245	2225
1	622	1974
2	2168	1700
done	5001	1696

prune473.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
done	15	13

end0.0ms

sample1.8s

Algorithm

intervals

Results

571.0ms	4187×	body	80	valid
481.0ms	1908×	body	640	valid
267.0ms	580×	body	1280	valid
153.0ms	452×	body	160	valid
149.0ms	873×	body	320	valid