Details

sample89.0ms

Algorithm

intervals

Results

21.0ms	278×	body	80	nan
20.0ms	58×	body	640	valid
16.0ms	36×	body	1280	valid
12.0ms	134×	body	80	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.8b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

9.0ms	(sqrt (+ x 1))
16.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
29.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ x 1))
33.0ms	(/ 1 (sqrt (+ x 1)))
30.0ms	(/ 1 (sqrt x))
76.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.1s

Counts

805 → 805

Iterations

Iter	Nodes
done	2000
2	2000
1	1435
0	651

prune8.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 18.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
2.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
79×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
42×	`prod-diff`
39×	`add-cube-cbrt`
12×	`distribute-lft-out` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `hypot-def` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 171

Calls

4 calls:

9.0ms	(sqrt (+ x 1))
80.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))
29.0ms	(- (sqrt (+ x 1)) (sqrt x))

series364.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1))
198.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
76.0ms	(* (sqrt x) (sqrt (+ x 1)))
57.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	2003
3	2003
2	1736
1	540
0	216

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 18.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
2.2b	(- (+ 1 x) x)

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

299×	`*-un-lft-identity`
150×	`times-frac`
104×	`add-sqr-sqrt`
101×	`distribute-lft-out`
87×	`sqrt-prod`
56×	`add-cube-cbrt`
48×	`associate-/l*`
40×	`distribute-lft-out--`
20×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
12×	`prod-diff`
9×	`add-log-exp`
8×	`pow1` `associate-/r/`
7×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r*`
6×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `fma-neg` `sqrt-div` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--`
1×	`sum-log` `sub-neg` `sqrt-unprod` `associate--l+` `*-commutative`

Counts

4 → 250

Calls

4 calls:

65.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
80.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))
30.0ms	(- (+ 1 x) x)

series348.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
211.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
61.0ms	(* (sqrt x) (sqrt (+ x 1)))
1.0ms	(- (+ 1 x) x)

simplify755.0ms

Counts

262 → 262

Iterations

Iter	Nodes
done	2001
2	2001
1	815
0	301

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.5b	(* (sqrt x) (sqrt x))
2.5b	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
9.5b	(* (/ (+ 1 0) (fma (+ x 1) (sqrt (+ x 1)) (* (sqrt x) x))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
58×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
44×	`sqrt-prod`
38×	`frac-times`
36×	`pow1`
32×	`flip3-+` `frac-add` `flip-+`
29×	`associate-l` `add-cube-cbrt`
28×	`associate-*r/`
19×	`swap-sqr`
17×	`flip3--` `flip--`
16×	`sqrt-pow1` `pow1/2` `associate-r`
13×	`times-frac` `add-cbrt-cube` `add-exp-log`
11×	`associate-*l/`
10×	`pow-prod-up` `unswap-sqr`
9×	`distribute-lft-out`
7×	`pow-prod-down`
6×	`pow-sqr` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod`
1×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `distribute-rgt-out--` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv`

Counts

4 → 211

Calls

4 calls:

24.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
8.0ms	(* (sqrt x) (sqrt x))
10.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
120.0ms	(* (/ (+ 1 0) (fma (+ x 1) (sqrt (+ x 1)) (* (sqrt x) x))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
16.0ms	(* (sqrt x) (sqrt x))
83.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
182.0ms	(* (/ (+ 1 0) (fma (+ x 1) (sqrt (+ x 1)) (* (sqrt x) x))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

simplify954.0ms

Counts

223 → 223

Iterations

Iter	Nodes
done	2000
2	2000
1	1415
0	359

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample2.2s

Algorithm

intervals

Results

602.0ms	1118×	body	1280	valid
499.0ms	8086×	body	80	nan
488.0ms	1853×	body	640	valid
307.0ms	4080×	body	80	valid
102.0ms	649×	body	320	valid
33.0ms	300×	body	160	valid