Details

sample43.0ms

Algorithm

intervals

Results

10.0ms	303×	body	80	nan
9.0ms	50×	body	1280	valid
5.0ms	36×	body	640	valid
5.0ms	135×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite50.0ms

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:

5.0ms	(sqrt (+ x 1.0))
44.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sqrt (+ x 1.0))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2301
2	786
1	324
0	141

prune236.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 27.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
4.1b	(- (+ x 1.0) x)

rewrite160.0ms

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:

5.0ms	(sqrt (+ x 1.0))
22.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
89.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms	(- (+ x 1.0) x)

series324.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
89.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
189.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify1.6s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
2	1734
1	562
0	221

prune620.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

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:

8.0ms	(sqrt (+ x 1.0))
24.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
34.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1.0))
94.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
206.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	4108
2	1217
1	396
0	165

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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)))

rewrite15.0ms

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:

5.0ms	(+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x))
0.0ms	(hypot (sqrt x) (sqrt 1.0))
9.0ms	(/ 1.0 (+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x)))

series1.9s

Counts

3 → 9

Calls

3 calls:

474.0ms	(+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x))
317.0ms	(hypot (sqrt x) (sqrt 1.0))
1.1s	(/ 1.0 (+ (hypot (sqrt x) (sqrt 1.0)) (sqrt x)))

simplify2.6s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1688
1	518
0	195

prune391.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes41.0ms

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

sample2.4s

Algorithm

intervals

Results

537.0ms	1657×	body	1280	valid
530.0ms	8149×	body	80	nan
485.0ms	624×	body	320	valid
305.0ms	1271×	body	640	valid
286.0ms	4137×	body	80	valid
32.0ms	311×	body	160	valid