Details

sample42.0ms

Algorithm

intervals

Results

17.0ms	247×	body	80	valid
1.0ms	4×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify8.0ms

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

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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:

19.0ms

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

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify1.8s

Counts

15 → 15

Iterations

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

prune106.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

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)))

rewrite128.0ms

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:

83.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
10.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
15.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
16.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
108.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
111.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
96.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.5s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1475
1	394
0	160

prune662.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

24.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
11.0ms	(+ x (/ (fabs (- y x)) 2.0))
9.0ms	(+ x (/ (fabs (- y x)) 2.0))
96.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
26.0ms	(+ x (/ (fabs (- y x)) 2.0))
30.0ms	(+ x (/ (fabs (- y x)) 2.0))
22.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1461
1	306
0	129

prune468.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize46.0ms

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

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

116×	`sqrt-div`
61×	`sqrt-prod`
59×	`sqrt-pow1`
54×	`pow1`
36×	`add-sqr-sqrt` `pow-prod-up`
35×	`flip3-+` `pow1/2` `flip-+`
32×	`frac-times`
26×	`*-un-lft-identity`
20×	`associate-l`
16×	`associate-*r/` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down` `associate-*l/`
8×	`associate-r`
6×	`pow-plus` `unswap-sqr`
5×	`distribute-lft-out`
4×	`rem-sqrt-square` `cube-unmult` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`

Counts

4 → 171

Calls

4 calls:

21.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
22.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
95.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
169.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
70.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
102.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
26.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify2.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2848
1	670
0	253

prune767.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.0b

regimes208.0ms

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

sample727.0ms

Algorithm

intervals

Results

326.0ms	7662×	body	80	valid
41.0ms	67×	body	2560	valid
39.0ms	108×	body	1280	valid
12.0ms	85×	body	640	valid
5.0ms	50×	body	320	valid
2.0ms	28×	body	160	valid