Details

sample78.0ms

Algorithm

intervals

Results

18.0ms	277×	body	80	nan
17.0ms	59×	body	640	valid
13.0ms	38×	body	1280	valid
10.0ms	134×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
3.0b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite98.0ms

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))
9.0ms	(/ 1 (sqrt (+ x 1)))
6.0ms	(/ 1 (sqrt x))
47.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1))
41.0ms	(/ 1 (sqrt (+ x 1)))
43.0ms	(/ 1 (sqrt x))
74.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.2s

Counts

805 → 805

Iterations

Iter	Nodes
done	2000
2	2000
1	1435
0	651

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.1b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
9.5b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

236×	`*-un-lft-identity`
209×	`add-sqr-sqrt`
189×	`prod-diff`
180×	`times-frac`
174×	`add-cube-cbrt`
110×	`sqrt-prod`
89×	`unpow-prod-down`
33×	`sqr-pow`
26×	`distribute-lft-out`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`difference-of-squares`
9×	`flip3-+` `flip-+` `div-inv`
7×	`associate-/r*` `fma-neg` `add-exp-log`
6×	`pow1`
5×	`add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

3 → 303

Calls

3 calls:

5.0ms	(sqrt (+ x 1))
14.0ms	(/ 1 (sqrt (+ x 1)))
51.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series189.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(sqrt (+ x 1))
49.0ms	(/ 1 (sqrt (+ x 1)))
99.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify1.4s

Counts

312 → 312

Iterations

Iter	Nodes
done	2003
3	2003
2	1883
1	949
0	401

prune1.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 18.1b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

65×	`unpow-prod-down`
56×	`prod-diff`
54×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
22×	`sqr-pow`
9×	`difference-of-squares`
8×	`distribute-lft-out`
7×	`fma-neg`
3×	`distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

1 → 90

Calls

1 calls:

38.0ms

(- (pow x -1/2) (pow (+ x 1) -1/2))

series122.0ms

Counts

1 → 3

Calls

1 calls:

122.0ms

(- (pow x -1/2) (pow (+ x 1) -1/2))

simplify937.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2003
3	2003
2	1016
1	414
0	188

prune244.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))
0.4b	(fma (pow x -1/2) (pow x -1/2) (* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2))))
7.0b	(- (* (/ 1 x) (pow x -1/2)) (/ (/ 1 (+ 1 x)) (sqrt (+ 1 x))))
15.7b	(/ (- (* (/ 1 x) (pow x -1/2)) (/ (/ 1 (+ 1 x)) (sqrt (+ 1 x)))) (fma (pow x -1/2) (pow x -1/2) (* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

244×	`times-frac`
209×	`*-un-lft-identity`
132×	`add-sqr-sqrt` `prod-diff`
120×	`add-cube-cbrt`
86×	`sqrt-prod`
44×	`distribute-lft-out`
27×	`associate-l`
18×	`associate-/r/`
15×	`add-exp-log`
11×	`flip3-+` `add-cbrt-cube` `flip-+` `div-inv`
6×	`pow1` `add-log-exp`
5×	`associate-r` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `div-exp` `associate-l/` `associate-/l*` `associate-/l/`
2×	`frac-times` `cbrt-undiv` `flip3--` `associate-*r/` `frac-sub` `cbrt-unprod` `flip--`
1×	`distribute-rgt-in` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `1-exp` `div-sub` `pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 256

Calls

4 calls:

115.0ms	(* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))
0.0ms	(fma (pow x -1/2) (pow x -1/2) (* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2))))
34.0ms	(- (* (/ 1 x) (pow x -1/2)) (/ (/ 1 (+ 1 x)) (sqrt (+ 1 x))))
82.0ms	(/ (- (* (/ 1 x) (pow x -1/2)) (/ (/ 1 (+ 1 x)) (sqrt (+ 1 x)))) (fma (pow x -1/2) (pow x -1/2) (* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))
163.0ms	(fma (pow x -1/2) (pow x -1/2) (* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2))))
95.0ms	(- (* (/ 1 x) (pow x -1/2)) (/ (/ 1 (+ 1 x)) (sqrt (+ 1 x))))
290.0ms	(/ (- (* (/ 1 x) (pow x -1/2)) (/ (/ 1 (+ 1 x)) (sqrt (+ 1 x)))) (fma (pow x -1/2) (pow x -1/2) (* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))))

simplify2.5s

Counts

268 → 268

Iterations

Iter	Nodes
done	2000
1	2000
0	877

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

regimes35.0ms

Accuracy

97.2% (0.5b remaining)

Error of 1.4b against oracle of 0.9b and baseline of 19.7b

bsearch31.0ms

Steps

Iters	Range		Point
6	3231.8276777318033	48819.349325626084	7750.30240499724

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample2.3s

Algorithm

intervals

Results

721.0ms	8141×	body	80	nan
545.0ms	1839×	body	640	valid
448.0ms	1108×	body	1280	valid
263.0ms	4109×	body	80	valid
128.0ms	630×	body	320	valid
35.0ms	314×	body	160	valid