Details

sample89.0ms

Algorithm

intervals

Results

25.0ms	50×	body	640	valid
22.0ms	139×	body	80	valid
12.0ms	31×	body	320	valid
11.0ms	17×	body	1280	valid
5.0ms	19×	body	160	valid

simplify643.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	475
9	475
8	357
7	164
6	102
5	81
4	65
3	45
2	35
1	21
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
3.0b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
534×	`add-sqr-sqrt`
484×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
71×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
10×	`add-log-exp`
7×	`associate-/r*` `add-exp-log`
5×	`add-cbrt-cube`
4×	`pow1` `difference-of-sqr-1`
3×	`expm1-log1p-u` `flip3--` `frac-add` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l*`
2×	`sum-log` `sub-neg` `diff-log` `div-exp` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 608

Calls

3 calls:

9.0ms	(/ 1 (- x 1))
47.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
245.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series167.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ 1 (- x 1))
31.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
113.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.8s

Counts

617 → 617

Iterations

Iter	Nodes
done	5000
2	2836
1	1097
0	476

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
3.0b	(+ (/ 1 (- x 1)) (- (/ 1 (+ x 1)) (/ 2 x)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

730×	`*-un-lft-identity`
713×	`times-frac`
539×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+r+`
94×	`distribute-lft-out`
71×	`div-inv`
58×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`fma-def`
21×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
10×	`add-log-exp`
7×	`associate-/r*` `difference-of-sqr-1` `add-exp-log`
5×	`add-cbrt-cube`
4×	`pow1` `flip3--` `flip--`
3×	`expm1-log1p-u` `frac-add` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sum-log` `sub-neg` `diff-log` `div-exp` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `associate-+r-` `frac-2neg` `1-exp` `pow-flip` `inv-pow`

Counts

3 → 622

Calls

3 calls:

16.0ms	(/ 1 (- x 1))
56.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
137.0ms	(+ (/ 1 (- x 1)) (- (/ 1 (+ x 1)) (/ 2 x)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ 1 (- x 1))
43.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
128.0ms	(+ (/ 1 (- x 1)) (- (/ 1 (+ x 1)) (/ 2 x)))

simplify3.3s

Counts

631 → 631

Iterations

Iter	Nodes
done	5000
2	3174
1	1439
0	644

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1 x) (* (+ x 1) 2))
0.0b	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
0.1b	(* (* (+ x 1) x) (- x 1))
16.3b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
37×	`prod-diff`
35×	`add-sqr-sqrt`
34×	`*-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`
7×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
2×	`difference-of-squares`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `fma-def` `frac-2neg` `fma-neg` `diff-log` `difference-of-sqr-1` `associate-l` `-commutative` `div-inv` `distribute-lft-out--`

Counts

4 → 177

Calls

4 calls:

7.0ms	(- (* 1 x) (* (+ x 1) 2))
122.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
69.0ms	(* (* (+ x 1) x) (- x 1))
49.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series248.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* 1 x) (* (+ x 1) 2))
87.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
130.0ms	(* (* (+ x 1) x) (- x 1))
2.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify1.8s

Counts

189 → 189

Iterations

Iter	Nodes
done	5001
1	1281
0	355

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1) x)
0.1b	(* (* (+ x 1) x) (- x 1))
0.5b	(/ 2 (* (* (+ x 1) x) (- x 1)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-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` `associate-r`
8×	`frac-times` `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` `difference-of-squares`
1×	`clear-num` `associate-/r*` `frac-2neg` `difference-of-sqr-1` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 113

Calls

3 calls:

24.0ms	(* (+ x 1) x)
32.0ms	(* (* (+ x 1) x) (- x 1))
30.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

series267.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (+ x 1) x)
109.0ms	(* (* (+ x 1) x) (- x 1))
82.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

simplify2.0s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
2	2775
1	630
0	207

prune375.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	1877×	body	640	valid
508.0ms	4097×	body	80	valid
341.0ms	937×	body	320	valid
326.0ms	606×	body	1280	valid
115.0ms	486×	body	160	valid