Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	241×	body	80	valid
1.0ms	5×	body	1280	valid
0.0ms	5×	body	320	valid
0.0ms	2×	body	2560	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid

simplify176.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	19	7
3	29	7
4	40	7
5	45	7
6	49	7
7	58	7
8	74	7
9	90	7
10	101	7
11	103	7
12	107	7
13	108	7
done	108	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r-` `flip3-+` `div-sub` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 13

Calls

1 calls:

29.0ms

(+ x (/ (- x y) 2.0))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(+ x (/ (- x y) 2.0))

simplify2.5s

Counts

16 → 16

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	34	178
1	92	171
2	244	157
3	682	157
4	3238	157
done	5002	157

prune48.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.2b	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity` `sqrt-prod`
28×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+r-` `pow-plus` `sqrt-unprod` `div-sub` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

22.0ms	(+ x (/ (- x y) 2.0))
54.0ms	(sqrt (+ x (/ (- x y) 2.0)))
55.0ms	(sqrt (+ x (/ (- x y) 2.0)))
294.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ x (/ (- x y) 2.0))
124.0ms	(sqrt (+ x (/ (- x y) 2.0)))
134.0ms	(sqrt (+ x (/ (- x y) 2.0)))
67.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

simplify1.5s

Counts

119 → 119

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	114	2202
1	232	1538
2	631	1434
3	1854	1375
done	5000	1349

prune261.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
0.1b	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
0.2b	(* (* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0))))) (sqrt (+ x (/ (- x y) 2.0))))
0.3b	(* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0)))))

rewrite767.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-div`
112×	`sqrt-prod`
97×	`sqrt-pow1`
75×	`pow1`
60×	`add-sqr-sqrt`
53×	`pow1/2`
43×	`pow-prod-up`
42×	`*-un-lft-identity`
35×	`flip3-+` `flip-+`
32×	`frac-times`
22×	`add-cube-cbrt`
20×	`swap-sqr`
17×	`associate-r`
16×	`associate-*l/`
13×	`pow-sqr`
12×	`pow-prod-down`
11×	`add-exp-log` `associate-l` `add-cbrt-cube` `unswap-sqr`
10×	`associate-*r/`
9×	`distribute-lft-out`
7×	`pow-plus`
4×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`pow2` `rem-square-sqrt`

Counts

4 → 211

Calls

4 calls:

41.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
56.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
406.0ms	(* (* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0))))) (sqrt (+ x (/ (- x y) 2.0))))
247.0ms	(* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

610.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
570.0ms	(sqrt (sqrt (+ x (/ (- x y) 2.0))))
59.0ms	(* (* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0))))) (sqrt (+ x (/ (- x y) 2.0))))
116.0ms	(* (sqrt (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (sqrt (+ x (/ (- x y) 2.0)))))

simplify3.3s

Counts

223 → 223

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	240	6073
1	504	3780
2	1306	3392
3	3668	3265
done	5001	3213

prune501.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ (/ (- x y) 2.0) x))) (sqrt (+ x (/ (- x y) 2.0))))
0.2b	(* (* (fabs (cbrt (+ (/ (- x y) 2.0) x))) (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (cbrt (+ x (/ (- x y) 2.0)))))
0.6b	(cbrt (+ (/ (- x y) 2.0) x))
0.6b	(cbrt (+ x (/ (- x y) 2.0)))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`associate-r`
16×	`add-sqr-sqrt`
14×	`sqrt-div`
12×	`cbrt-prod` `add-cube-cbrt` `sqrt-prod`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`cbrt-div` `associate-*r/`
9×	`flip3-+` `flip-+`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out` `add-log-exp`
2×	`pow1/3` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

134.0ms	(* (fabs (cbrt (+ (/ (- x y) 2.0) x))) (sqrt (+ x (/ (- x y) 2.0))))
239.0ms	(* (* (fabs (cbrt (+ (/ (- x y) 2.0) x))) (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (cbrt (+ x (/ (- x y) 2.0)))))
53.0ms	(cbrt (+ (/ (- x y) 2.0) x))
39.0ms	(cbrt (+ x (/ (- x y) 2.0)))

series1.9s

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (fabs (cbrt (+ (/ (- x y) 2.0) x))) (sqrt (+ x (/ (- x y) 2.0))))
653.0ms	(* (* (fabs (cbrt (+ (/ (- x y) 2.0) x))) (sqrt (+ x (/ (- x y) 2.0)))) (sqrt (cbrt (+ x (/ (- x y) 2.0)))))
585.0ms	(cbrt (+ (/ (- x y) 2.0) x))
560.0ms	(cbrt (+ x (/ (- x y) 2.0)))

simplify3.6s

Counts

98 → 98

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	247	2734
1	564	2547
2	1585	2333
3	4721	2227
done	5002	2187

prune574.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	7	7
done	7	7

end0.0ms

sample983.0ms

Algorithm

intervals

Results

364.0ms	79×	body	320	valid
284.0ms	7418×	body	80	valid
32.0ms	237×	body	1280	valid
15.0ms	137×	body	640	valid
14.0ms	90×	body	2560	valid
2.0ms	42×	body	160	valid