Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	66×	body	1280	valid
7.0ms	249×	body	80	nan
4.0ms	37×	body	640	valid
4.0ms	123×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	5×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series15.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.0s

Counts

41 → 41

Iterations

Useful iterations: 3 (292.0ms)

Iter	Nodes	Cost
0	116	606
1	288	568
2	984	552
3	3607	528
done	5000	528

prune85.0ms

Filtered

30 candidates to 41 candidates (-36.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 80

Calls

3 calls:

9.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
3.0ms	(sqrt (+ x 1.0))
13.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series25.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
4.0ms	(sqrt (+ x 1.0))
10.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify451.0ms

Counts

89 → 89

Iterations

Useful iterations: done (448.0ms)

Iter	Nodes	Cost
0	202	1513
1	516	1285
2	1715	1192
done	5000	1190

prune171.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	86	7	93

Merged error: 0.0b

Counts

93 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 0 1.0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
13×	`cbrt-prod`
12×	`times-frac`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `flip-+`
4×	`associate-/l*` `add-log-exp`
3×	`associate-l` `associate-/r*` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 92

Calls

4 calls:

14.0ms	(/ (+ 0 1.0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
9.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series75.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (+ 0 1.0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
12.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
7.0ms	(cbrt (+ x 1.0))
7.0ms	(cbrt (+ x 1.0))

simplify921.0ms

Counts

104 → 104

Iterations

Useful iterations: done (917.0ms)

Iter	Nodes	Cost
0	343	2943
1	924	2655
2	3903	2452
done	5000	2445

prune390.0ms

Filtered

86 candidates to 104 candidates (-20.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Merged error: 0.0b

Counts

111 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (+ 0 1.0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
78×	`*-un-lft-identity`
34×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`flip3-+` `swap-sqr` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`times-frac` `associate-r/` `associate-l/` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 139

Calls

4 calls:

13.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(/ (+ 0 1.0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
23.0ms	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(/ (+ 0 1.0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
7.0ms	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify644.0ms

Counts

151 → 151

Iterations

Useful iterations: done (638.0ms)

Iter	Nodes	Cost
0	274	3739
1	697	2488
2	2670	2263
done	5000	2247

prune281.0ms

Filtered

91 candidates to 151 candidates (-65.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	151	7	158

Merged error: 0.0b

Counts

158 → 7

regimes101.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	12	9
done	12	9

end0.0ms

sample1.1s

Algorithm

intervals

Results

249.0ms	1738×	body	1280	valid
240.0ms	8058×	body	80	nan
140.0ms	1221×	body	640	valid
131.0ms	4125×	body	80	valid
60.0ms	625×	body	320	valid
16.0ms	291×	body	160	valid

Details

sample38.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite13.0ms

series15.0ms

simplify1.0s

prune85.0ms

localize8.0ms

rewrite29.0ms

series25.0ms

simplify451.0ms

prune171.0ms

localize16.0ms

rewrite33.0ms

series75.0ms

simplify921.0ms

prune390.0ms

localize11.0ms

rewrite77.0ms

series42.0ms

simplify644.0ms

prune281.0ms

regimes101.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling