Details

sample78.0ms

Algorithm

intervals

Results

19.0ms	53×	body	1280	valid
17.0ms	259×	body	80	nan
12.0ms	42×	body	640	valid
10.0ms	137×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize38.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (sqrt (+ x 1)) (sqrt x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
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 → 71

Calls

1 calls:

64.0ms

(- (sqrt (+ x 1)) (sqrt x))

series82.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

(- (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
4	2000
3	1574
2	519
1	241
0	108

prune633.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 28.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ 1 x)))
0.0b	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
2.2b	(- (+ 1 x) x)

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
44×	`distribute-lft-out`
43×	`add-sqr-sqrt`
36×	`times-frac`
35×	`sqrt-prod`
27×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `fma-def` `associate-/l`
5×	`add-cbrt-cube` `add-exp-log`
4×	`fma-neg`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sum-log` `flip3-+` `flip3--` `diff-log` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sub-neg` `frac-2neg` `div-sub` `div-exp` `associate--l+` `div-inv`

Counts

3 → 127

Calls

3 calls:

23.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
126.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
34.0ms	(- (+ 1 x) x)

series192.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
122.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
2.0ms	(- (+ 1 x) x)

simplify1.2s

Counts

136 → 136

Iterations

Iter	Nodes
done	2002
3	2002
2	1140
1	396
0	157

prune967.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
17×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`add-exp-log`
7×	`fma-def`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u` `pow1`
4×	`insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `log1p-udef` `expm1-log1p` `clear-num` `sum-log` `frac-2neg` `1-exp` `log1p-expm1` `div-inv` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 96

Calls

4 calls:

40.0ms	(+ (sqrt (+ 1 x)) (sqrt x))
1.0ms	(log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
0.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))
49.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (sqrt (+ 1 x)) (sqrt x))
156.0ms	(log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
226.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))
99.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	2000
4	2000
3	1201
2	563
1	249
0	121

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
0.1b	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
0.1b	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
0.3b	(* (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity`
290×	`sqrt-prod`
168×	`times-frac`
136×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
43×	`swap-sqr`
31×	`pow1`
27×	`sqrt-pow1` `associate-r` `associate-l`
16×	`unswap-sqr`
14×	`add-exp-log` `associate-/r/`
12×	`associate-/r*`
11×	`pow-flip` `inv-pow`
10×	`add-cbrt-cube`
9×	`pow1/2` `pow-prod-up` `div-inv`
7×	`flip3-+` `flip-+`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 290

Calls

4 calls:

45.0ms	(sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
45.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
52.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
208.0ms	(* (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
83.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
118.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
92.0ms	(* (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))

simplify1.1s

Counts

302 → 302

Iterations

Iter	Nodes
done	2000
3	2000
2	1017
1	466
0	235

prune3.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

747.0ms	1241×	body	640	valid
521.0ms	1731×	body	1280	valid
472.0ms	8060×	body	80	nan
398.0ms	4070×	body	80	valid
148.0ms	649×	body	320	valid
33.0ms	309×	body	160	valid