Details

sample57.0ms

Algorithm

intervals

Results

12.0ms	248×	body	80	nan
11.0ms	49×	body	1280	valid
9.0ms	48×	body	640	valid
6.0ms	132×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
1.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 92

Calls

2 calls:

11.0ms	(sqrt (+ x 1))
79.0ms	(- (sqrt (+ x 1)) (sqrt x))

series130.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(sqrt (+ x 1))
89.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
4	4262
3	1554
2	618
1	294
0	134

prune228.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 28.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ 1 x)))
0.0b	(sqrt (+ 1 x))
0.0b	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
1.5b	(- (+ 1 x) x)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
45×	`distribute-lft-out`
39×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `fma-def` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `hypot-1-def` `div-inv`

Counts

4 → 149

Calls

4 calls:

40.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
15.0ms	(sqrt (+ 1 x))
124.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
44.0ms	(- (+ 1 x) x)

series211.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
27.0ms	(sqrt (+ 1 x))
99.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
2.0ms	(- (+ 1 x) x)

simplify2.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
3	2889
2	1141
1	455
0	186

prune558.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ 1 x)))
0.0b	(sqrt (+ 1 x))
0.1b	(/ (posit16->real (real->posit16 1)) (+ (sqrt x) (sqrt (+ 1 x))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
27×	`sqrt-prod`
22×	`add-sqr-sqrt`
21×	`distribute-lft-out`
18×	`times-frac`
17×	`add-cube-cbrt`
6×	`associate-/r*` `fma-def`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-1-def` `div-inv`

Counts

3 → 89

Calls

3 calls:

38.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
14.0ms	(sqrt (+ 1 x))
67.0ms	(/ (posit16->real (real->posit16 1)) (+ (sqrt x) (sqrt (+ 1 x))))

series191.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
42.0ms	(sqrt (+ 1 x))
84.0ms	(/ (posit16->real (real->posit16 1)) (+ (sqrt x) (sqrt (+ 1 x))))

simplify3.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5020
4	3487
3	1830
2	644
1	281
0	132

prune768.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.0b	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `sqrt-prod`
18×	`times-frac`
17×	`distribute-lft-out`
16×	`add-cube-cbrt`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`flip3-+` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `hypot-def`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `log1p-expm1` `div-inv` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 93

Calls

4 calls:

14.0ms	(sqrt (+ x 1))
1.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
44.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1))
174.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
216.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
73.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	1818
2	708
1	287
0	143

prune457.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

797.0ms	1671×	body	1280	valid
453.0ms	8127×	body	80	nan
224.0ms	4169×	body	80	valid
180.0ms	1227×	body	640	valid
65.0ms	618×	body	320	valid
22.0ms	315×	body	160	valid