Details

sample56.0ms

Algorithm

intervals

Results

15.0ms	50×	body	640	valid
11.0ms	139×	body	80	valid
7.0ms	31×	body	320	valid
6.0ms	17×	body	1280	valid
3.0ms	19×	body	160	valid

simplify279.0ms

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

localize18.0ms

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)))

rewrite636.0ms

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:

8.0ms	(/ 1 (- x 1))
64.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
539.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ 1 (- x 1))
47.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
139.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.7s

Counts

617 → 617

Iterations

Iter	Nodes
done	5000
2	2836
1	1097
0	476

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

1474×	`add-sqr-sqrt`
1453×	`times-frac`
1452×	`*-un-lft-identity`
936×	`prod-diff`
816×	`add-cube-cbrt`
353×	`associate--r+`
281×	`difference-of-squares`
197×	`distribute-lft-out--`
120×	`div-inv`
82×	`difference-of-sqr-1` `associate-/r/`
44×	`distribute-lft-out`
31×	`fma-neg`
30×	`flip3--` `flip--`
14×	`flip3-+` `flip-+`
10×	`add-log-exp`
7×	`associate-/r*` `add-exp-log`
5×	`add-cbrt-cube` `frac-sub`
4×	`pow1` `diff-log`
3×	`expm1-log1p-u` `sub-neg` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`div-exp`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-flip` `inv-pow` `associate--r-`

Counts

3 → 1080

Calls

3 calls:

8.0ms	(/ 1 (- x 1))
29.0ms	(- (/ 2 x) (/ 1 (- x 1)))
141.0ms	(- (/ 1 (+ x 1)) (- (/ 2 x) (/ 1 (- x 1))))

series180.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1 (- x 1))
30.0ms	(- (/ 2 x) (/ 1 (- x 1)))
131.0ms	(- (/ 1 (+ x 1)) (- (/ 2 x) (/ 1 (- x 1))))

simplify2.3s

Counts

1089 → 1089

Iterations

Iter	Nodes
done	5000
1	2537
0	1015

prune5.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

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))

rewrite190.0ms

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:

16.0ms	(- (* 1 x) (* (+ x 1) 2))
101.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
33.0ms	(* (* (+ x 1) x) (- x 1))
32.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series210.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* 1 x) (* (+ x 1) 2))
74.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
105.0ms	(* (* (+ x 1) x) (- x 1))
3.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify1.5s

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

localize16.0ms

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)))

rewrite79.0ms

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:

15.0ms	(* (+ x 1) x)
36.0ms	(* (* (+ x 1) x) (- x 1))
24.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* (+ x 1) x)
125.0ms	(* (* (+ x 1) x) (- x 1))
83.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

simplify2.0s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
2	2775
1	630
0	207

prune513.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample2.0s

Algorithm

intervals

Results

732.0ms	606×	body	1280	valid
520.0ms	1877×	body	640	valid
289.0ms	4097×	body	80	valid
248.0ms	937×	body	320	valid
57.0ms	486×	body	160	valid