Details

sample47.0ms

Algorithm

intervals

Results

14.0ms	62×	body	1280	valid
9.0ms	213×	body	80	nan
6.0ms	134×	body	80	valid
5.0ms	30×	body	640	valid
3.0ms	26×	body	320	valid
0.0ms	4×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `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` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 91

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
37.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series145.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(sqrt (+ x 1.0))
101.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify598.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2001
2	786
1	324
0	141

prune304.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 28.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(sqrt (+ x 1.0))
0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(- (+ x 1.0) x)

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
46×	`distribute-lft-out`
40×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
7×	`fma-def`
6×	`associate-/r` `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/` `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-def` `div-inv`

Counts

4 → 148

Calls

4 calls:

21.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
6.0ms	(sqrt (+ x 1.0))
102.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms	(- (+ x 1.0) x)

series242.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
30.0ms	(sqrt (+ x 1.0))
144.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify607.0ms

Counts

160 → 160

Iterations

Iter	Nodes
done	2000
2	1738
1	562
0	221

prune437.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`distribute-lft-out`
20×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
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/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 88

Calls

3 calls:

23.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
5.0ms	(sqrt (+ x 1.0))
36.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series314.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
46.0ms	(sqrt (+ x 1.0))
167.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify802.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2000
2	1217
1	396
0	165

prune324.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x))
0.0b	(hypot (sqrt x) (sqrt 1.0))
0.2b	(/ 1.0 (+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `add-log-exp`
4×	`associate-/r*`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `hypot-udef` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 65

Calls

3 calls:

8.0ms	(+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x))
0.0ms	(hypot (sqrt x) (sqrt 1.0))
14.0ms	(/ 1.0 (+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x)))

series1.7s

Counts

3 → 9

Calls

3 calls:

401.0ms	(+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x))
319.0ms	(hypot (sqrt x) (sqrt 1.0))
953.0ms	(/ 1.0 (+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x)))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
2	1688
1	518
0	195

prune262.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	8
1	8
0	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

904.0ms	1749×	body	1280	valid
472.0ms	7964×	body	80	nan
316.0ms	4127×	body	80	valid
260.0ms	1191×	body	640	valid
217.0ms	624×	body	320	valid
58.0ms	309×	body	160	valid