Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	243×	body	80	valid
1.0ms	4×	body	1280	valid
1.0ms	4×	body	640	valid
0.0ms	2×	body	2560	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

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-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

9.0ms

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

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

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

simplify2.0s

Counts

20 → 20

Iterations

Iter	Nodes
done	5000
4	1858
3	630
2	234
1	89
0	33

prune102.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

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` `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 → 121

Calls

4 calls:

10.0ms	(+ x (/ (fabs (- y x)) 2.0))
25.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
16.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
70.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ x (/ (fabs (- y x)) 2.0))
89.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
59.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
26.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	1379
1	318
0	135

prune619.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

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-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

10.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
13.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
13.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
12.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
58.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
71.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
76.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	3214
2	728
1	216
0	89

prune640.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
0.5b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.5b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.5b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cbrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

92.0ms	(* (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
15.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
9.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
14.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
104.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
74.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
66.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.6s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	1614
1	434
0	189

prune832.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes253.0ms

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

sample1.0s

Algorithm

intervals

Results

663.0ms	7681×	body	80	valid
54.0ms	118×	body	1280	valid
13.0ms	53×	body	2560	valid
10.0ms	78×	body	640	valid
4.0ms	40×	body	320	valid
2.0ms	30×	body	160	valid