Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	282×	body	80	nan
8.0ms	63×	body	1280	valid
5.0ms	46×	body	640	valid
4.0ms	116×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
3.1b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite74.0ms

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` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

6.0ms	(sqrt (+ 1.0 x))
64.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series147.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(sqrt (+ 1.0 x))
109.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify711.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1090
1	323
0	139

prune267.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
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 → 94

Calls

3 calls:

7.0ms	(sqrt (+ 1.0 x))
32.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
93.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

series350.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ 1.0 x))
94.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
217.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify1.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2042
1	439
0	173

prune471.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
708×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
270×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
8×	`hypot-def`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 461

Calls

4 calls:

68.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
46.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
59.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
132.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

238.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
237.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
498.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
215.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify1.9s

Counts

473 → 473

Iterations

Iter	Nodes
done	5000
2	4313
1	1103
0	448

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (log1p (expm1 (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.4b	(expm1 (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
94×	`sqrt-prod`
54×	`times-frac`
50×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
36×	`distribute-lft-out`
18×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`sqrt-div` `associate-/l*`
5×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `associate-/r/` `hypot-def` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `expm1-udef`

Counts

4 → 145

Calls

4 calls:

44.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
62.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
49.0ms	(/ (log1p (expm1 (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.0ms	(expm1 (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series4.2s

Counts

4 → 12

Calls

4 calls:

239.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
545.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
2.3s	(/ (log1p (expm1 (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
1.1s	(expm1 (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.4s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	3772
1	886
0	362

prune740.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
2	13
1	12
0	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

453.0ms	663×	body	320	valid
309.0ms	8079×	body	80	nan
287.0ms	1247×	body	640	valid
286.0ms	1686×	body	1280	valid
138.0ms	4121×	body	80	valid
19.0ms	283×	body	160	valid