Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	102×	body	1280	valid
4.0ms	132×	body	80	valid
1.0ms	12×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6
done	37	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize8.0ms

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	(/ 1.0 (hypot 1.0 x))
1.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite38.0ms

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:

10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
77.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(/ 1.0 (hypot 1.0 x))
88.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify68.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463
done	5001	463

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
42.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
15.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
82.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
159.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify51.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	423	1277
1	1641	1179
2	5001	1174
done	5001	1174

prune297.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(* (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
0.6b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

793×	`associate-*r/`
352×	`frac-times`
312×	`frac-add`
212×	`flip3--` `flip--`
152×	`associate-*l/`
127×	`flip3-+` `flip-+`
13×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`cube-div` `sqr-pow`
4×	`associate-r` `difference-of-squares`
3×	`pow-unpow` `associate-l` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
2×	`pow-pow` `pow-prod-down` `frac-sub` `distribute-lft-out`
1×	`difference-cubes` `cbrt-undiv` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `div-exp` `sum-log` `*-commutative` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 302

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
206.0ms	(* (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
12.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
19.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series404.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
193.0ms	(* (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
41.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
68.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify189.0ms

Counts

314 → 314

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	3830	15113
1	5003	15026
done	5003	15026

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(* (/ (sqrt (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
0.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite361.0ms

Algorithm

rewrite-expression-head

Rules

330×	`sqrt-prod`
302×	`add-sqr-sqrt`
300×	`times-frac`
242×	`*-un-lft-identity`
136×	`add-cube-cbrt`
94×	`swap-sqr`
48×	`associate-r` `associate-l`
45×	`distribute-lft-out`
25×	`unswap-sqr`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-log-exp`
9×	`associate-*r/`
8×	`sqrt-div` `associate--l+` `associate-/r/`
6×	`sub-neg`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `distribute-rgt-in` `sqrt-undiv` `flip3--` `distribute-lft-in` `div-exp` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `div-inv`
2×	`diff-log`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `sqrt-unprod` `pow-prod-down` `associate-l/` `sum-log` `rem-square-sqrt` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 289

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
304.0ms	(* (/ (sqrt (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
15.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
15.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
168.0ms	(* (/ (sqrt (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
40.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify153.0ms

Counts

301 → 301

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	879	11585
1	4263	10037
2	5001	9916
done	5001	9916

prune575.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.1b

regimes81.0ms

Accuracy

0% (0.3b remaining)

Error of 15.4b against oracle of 15.1b and baseline of 15.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15
done	21	15

end0.0ms

sample846.0ms

Algorithm

intervals

Results

458.0ms	2809×	body	1280	valid
122.0ms	4070×	body	80	valid
85.0ms	673×	body	640	valid
25.0ms	287×	body	320	valid
9.0ms	161×	body	160	valid