Details

sample105.0ms

Algorithm

intervals

Results

30.0ms	71×	body	640	valid
21.0ms	42×	body	1280	valid
21.0ms	258×	body	80	nan
11.0ms	117×	body	80	valid
3.0ms	13×	body	320	valid
3.0ms	13×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite133.0ms

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:

5.0ms	(sqrt (+ x 1))
10.0ms	(/ 1 (sqrt (+ x 1)))
11.0ms	(/ 1 (sqrt x))
73.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1))
33.0ms	(/ 1 (sqrt (+ x 1)))
47.0ms	(/ 1 (sqrt x))
90.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.2s

Counts

805 → 805

Iterations

Iter	Nodes
done	2000
2	2000
1	1435
0	651

prune2.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 21.2b

localize27.0ms

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))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
3.2b	(- (sqrt (+ x 1)) (sqrt x))

rewrite140.0ms

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:

5.0ms	(sqrt (+ x 1))
84.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
19.0ms	(* (sqrt x) (sqrt (+ x 1)))
30.0ms	(- (sqrt (+ x 1)) (sqrt x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1))
196.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
69.0ms	(* (sqrt x) (sqrt (+ x 1)))
73.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

183 → 183

Iterations

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

prune605.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 20.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
2.2b	(- (+ 1 x) x)

rewrite209.0ms

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:

74.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
87.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))
26.0ms	(- (+ 1 x) x)

series397.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
237.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
69.0ms	(* (sqrt x) (sqrt (+ x 1)))
1.0ms	(- (+ 1 x) x)

simplify1.0s

Counts

262 → 262

Iterations

Iter	Nodes
done	2001
2	2001
1	815
0	301

prune828.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(* (/ (+ 1 0) (sqrt x)) (/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1))))
0.2b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1)))
0.2b	(/ (+ 1 0) (sqrt x))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

769×	`*-un-lft-identity`
716×	`times-frac`
435×	`sqrt-prod`
376×	`add-sqr-sqrt`
296×	`add-cube-cbrt`
258×	`distribute-lft-out`
174×	`associate-r`
54×	`add-exp-log`
36×	`associate-/r/`
34×	`add-cbrt-cube`
31×	`associate-/l*`
28×	`associate-l`
26×	`div-exp`
21×	`unswap-sqr`
20×	`div-inv`
19×	`associate-/r*` `flip3-+` `flip-+`
14×	`cbrt-undiv`
10×	`prod-exp`
7×	`pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `sqrt-div` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 574

Calls

4 calls:

53.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
101.0ms	(* (/ (+ 1 0) (sqrt x)) (/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1))))
57.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1)))
14.0ms	(/ (+ 1 0) (sqrt x))

series549.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
250.0ms	(* (/ (+ 1 0) (sqrt x)) (/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1))))
190.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1)))
32.0ms	(/ (+ 1 0) (sqrt x))

simplify1.1s

Counts

586 → 586

Iterations

Iter	Nodes
done	2001
2	2001
1	1529
0	497

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	14

end0.0ms

sample2.4s

Algorithm

intervals

Results

819.0ms	1833×	body	640	valid
493.0ms	8102×	body	80	nan
412.0ms	1110×	body	1280	valid
294.0ms	4151×	body	80	valid
128.0ms	609×	body	320	valid
35.0ms	297×	body	160	valid