Details

sample40.0ms

Algorithm

intervals

Results

19.0ms	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

localize8.0ms

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))))))

rewrite25.0ms

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))
10.0ms	(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))))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify506.0ms

Counts

78 → 78

Iterations

Useful iterations: done (504.0ms)

Iter	Nodes	Cost
0	112	1034
1	238	951
2	623	887
3	1695	885
done	5000	877

prune161.0ms

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

localize13.0ms

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

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/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 72

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
38.0ms	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify410.0ms

Counts

84 → 84

Iterations

Useful iterations: done (407.0ms)

Iter	Nodes	Cost
0	114	2183
1	315	2113
2	1115	1891
done	5000	1723

prune453.0ms

Filtered

61 candidates to 84 candidates (-37.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 16.1b

Counts

89 → 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)))

rewrite34.0ms

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)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
35.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
9.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify741.0ms

Counts

103 → 103

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	149	2387
1	366	2296
2	955	2158
3	3220	2158
done	5001	2157

prune277.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

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

localize20.0ms

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))))

rewrite58.0ms

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:

13.0ms	(/ (- (* 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))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
61.0ms	(/ (/ (- (* 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)))))))
16.0ms	(* (/ 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))))

simplify959.0ms

Counts

265 → 265

Iterations

Useful iterations: 2 (356.0ms)

Iter	Nodes	Cost
0	360	11022
1	1023	10405
2	4320	9417
done	5000	9417

prune1.1s

Filtered

174 candidates to 265 candidates (-52.3%)

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

regimes408.0ms

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

691.0ms	2911×	body	1280	valid
170.0ms	3981×	body	80	valid
118.0ms	631×	body	640	valid
39.0ms	304×	body	320	valid
15.0ms	173×	body	160	valid

Details

sample40.0ms

simplify19.0ms

prune3.0ms

localize8.0ms

rewrite25.0ms

series41.0ms

simplify506.0ms

prune161.0ms

localize13.0ms

rewrite27.0ms

series58.0ms

simplify410.0ms

prune453.0ms

localize12.0ms

rewrite34.0ms

series66.0ms

simplify741.0ms

prune277.0ms

localize20.0ms

rewrite58.0ms

series125.0ms

simplify959.0ms

prune1.1s

regimes408.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling