Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	244×	body	80	valid
1.0ms	4×	body	1280	valid
1.0ms	3×	body	2560	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	320	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 18

Calls

1 calls:

13.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify3.7s

Counts

21 → 21

Iterations

Iter	Nodes
done	5000
5	4267
4	1455
3	564
2	235
1	90
0	34

prune137.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

69.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
9.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
8.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
13.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
66.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
75.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
72.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify2.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	2789
2	1035
1	403
0	166

prune622.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `cbrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

4.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
4.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
4.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
66.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
63.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
61.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	1836
2	615
1	217
0	90

prune671.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.1b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.1b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `hypot-def` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `times-frac` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 125

Calls

4 calls:

7.0ms	(+ x (/ (fabs (- y x)) 2.0))
8.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
12.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
78.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ x (/ (fabs (- y x)) 2.0))
61.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
77.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
28.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify2.6s

Counts

137 → 137

Iterations

Iter	Nodes
done	5002
3	2528
2	815
1	316
0	138

prune517.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes132.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
1	8
0	7

end0.0ms

sample588.0ms

Algorithm

intervals

Results

378.0ms	7689×	body	80	valid
20.0ms	113×	body	1280	valid
12.0ms	57×	body	2560	valid
11.0ms	78×	body	640	valid
5.0ms	42×	body	320	valid
2.0ms	21×	body	160	valid