Details

sample62.0ms

Algorithm

intervals

Results

30.0ms	87×	body	1280	valid
8.0ms	130×	body	80	valid
5.0ms	20×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot 1.0 x)
8.0ms	(/ 1.0 (hypot 1.0 x))
21.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

94.0ms	(hypot 1.0 x)
152.0ms	(/ 1.0 (hypot 1.0 x))
404.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
577.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

97 → 97

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	225	2149
1	536	1724
2	1590	1489
done	5001	1355

prune436.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `sqrt-prod` `flip--` `flip-+`

Counts

4 → 89

Calls

4 calls:

20.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series898.0ms

Counts

4 → 12

Calls

4 calls:

356.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
163.0ms	(/ 1.0 (hypot 1.0 x))
186.0ms	(/ 1.0 (hypot 1.0 x))
193.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	191	1467
1	480	1369
2	1585	1266
done	5001	1250

prune505.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
2.1b	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
18.2b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 137

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series777.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1.0 (hypot 1.0 x))
305.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
167.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
171.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify1.9s

Counts

149 → 149

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	227	2365
1	596	1929
2	1989	1722
done	5000	1687

prune525.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
2.1b	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

56×	`prod-diff`
53×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
46×	`add-cube-cbrt`
37×	`unpow-prod-down`
22×	`sqr-pow`
18×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
8×	`cube-mult` `unpow3` `cube-prod`
7×	`pow1` `fma-neg`
6×	`associate-/r` `associate-/l` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `pow-pow` `frac-2neg` `div-exp` `associate-*l/` `pow-exp` `clear-num` `div-inv` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(/ 1.0 (hypot 1.0 x))
30.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
47.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ 1.0 (hypot 1.0 x))
164.0ms	(/ 1.0 (hypot 1.0 x))
377.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
537.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify1.8s

Counts

180 → 180

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	300	6560
1	739	4285
2	2306	3343
done	5001	2607

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.0b

regimes456.0ms

Accuracy

0% (0.2b remaining)

Error of 15.4b against oracle of 15.2b and baseline of 15.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	70
1	29	70
done	29	70

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2825×	body	1280	valid
629.0ms	4040×	body	80	valid
160.0ms	665×	body	640	valid
71.0ms	161×	body	160	valid
46.0ms	309×	body	320	valid