Details

sample45.0ms

Algorithm

intervals

Results

24.0ms	82×	body	1280	valid
6.0ms	132×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	9×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	23	12
3	27	12
4	29	12
5	34	12
6	36	12
done	36	12

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: 16.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

78 → 78

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	112	1034
1	238	962
2	580	890
3	1444	886
4	4217	882
done	5000	881

prune156.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 16.1b

Counts

79 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`pow1` `associate-/r*`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`+-commutative` `flip3--` `sum-log` `associate-/r/` `flip--` `associate-/l/` `associate--r+`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 74

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
4.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
36.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

86 → 86

Iterations

Useful iterations: 3 (384.0ms)

Iter	Nodes	Cost
0	117	2197
1	322	2123
2	1124	1929
3	4612	1894
done	5000	1894

prune256.0ms

Filtered

62 candidates to 86 candidates (-38.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 16.1b

Counts

91 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
30×	`times-frac`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `distribute-lft-out--`
4×	`associate-/r*`
3×	`flip3-+` `flip-+`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `div-inv`

Counts

4 → 91

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
40.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify926.0ms

Counts

103 → 103

Iterations

Useful iterations: done (922.0ms)

Iter	Nodes	Cost
0	149	2387
1	366	2304
2	958	2160
3	2906	2158
done	5000	2157

prune273.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	103	7	110

Merged error: 16.1b

Counts

110 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
0.0b	(/ (/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
1.6b	(- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac`
206×	`*-un-lft-identity`
122×	`add-sqr-sqrt`
110×	`add-cube-cbrt`
48×	`distribute-lft-out`
26×	`associate-/l*` `difference-of-squares`
23×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1` `div-inv`
8×	`cbrt-undiv` `div-exp` `associate-/r*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 253

Calls

4 calls:

15.0ms	(/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
17.0ms	(/ (/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
4.0ms	(- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
67.0ms	(/ (/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
14.0ms	(- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

simplify1.1s

Counts

265 → 265

Iterations

Useful iterations: 2 (332.0ms)

Iter	Nodes	Cost
0	360	11022
1	1023	10455
2	4575	9445
done	5000	9445

prune1.3s

Filtered

182 candidates to 265 candidates (-45.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	259	6	265
Fresh	4	1	5
Picked	1	0	1
Done	1	0	1
Total	265	7	272

Merged error: 15.7b

Counts

272 → 7

regimes401.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	66
1	29	66
done	29	66

end0.0ms

sample1.2s

Algorithm

intervals

Results

682.0ms	2911×	body	1280	valid
173.0ms	3981×	body	80	valid
117.0ms	631×	body	640	valid
39.0ms	304×	body	320	valid
15.0ms	173×	body	160	valid

Details

sample45.0ms

simplify19.0ms

prune3.0ms

localize9.0ms

rewrite26.0ms

series42.0ms

simplify1.2s

prune156.0ms

localize12.0ms

rewrite27.0ms

series60.0ms

simplify1.2s

prune256.0ms

localize12.0ms

rewrite35.0ms

series68.0ms

simplify926.0ms

prune273.0ms

localize18.0ms

rewrite61.0ms

series123.0ms

simplify1.1s

prune1.3s

regimes401.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling