Details

sample37.0ms

Algorithm

intervals

Results

12.0ms	243×	body	80	valid
8.0ms	4×	body	640	valid
1.0ms	4×	body	1280	valid
1.0ms	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

prune9.0ms

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))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 12

Calls

1 calls:

17.0ms

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

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

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

simplify1.2s

Counts

15 → 15

Iterations

Iter	Nodes
done	5000
4	1695
3	592
2	215
1	84
0	31

prune86.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite149.0ms

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×	`frac-times` `add-cbrt-cube` `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 → 95

Calls

4 calls:

99.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
16.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
13.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
96.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
97.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
107.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify788.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1475
1	394
0	160

prune728.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

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))))

rewrite193.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 106

Calls

4 calls:

17.0ms	(+ x (/ (fabs (- y x)) 2.0))
27.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
29.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
116.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ x (/ (fabs (- y x)) 2.0))
72.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
80.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
22.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1458
1	305
0	129

prune498.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.3b	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
0.5b	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

121×	`sqrt-prod`
74×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
36×	`sqrt-div`
29×	`unpow-prod-down` `cube-prod`
26×	`associate-r`
25×	`add-cube-cbrt`
24×	`unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`associate-l` `add-exp-log`
9×	`flip3-+` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube` `distribute-lft-out`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-l/` `pow-exp` `associate-r/`
1×	`*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 169

Calls

4 calls:

33.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
31.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
161.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
25.0ms	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

series355.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
73.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
21.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
155.0ms	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

simplify2.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3415
1	666
0	231

prune929.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes230.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	8
1	8
0	7

end0.0ms

sample900.0ms

Algorithm

intervals

Results

632.0ms	7681×	body	80	valid
19.0ms	118×	body	1280	valid
11.0ms	53×	body	2560	valid
9.0ms	78×	body	640	valid
4.0ms	40×	body	320	valid
2.0ms	30×	body	160	valid