Details

sample14.0ms

Algorithm

intervals

Results

4.0ms	245×	body	80	valid
1.0ms	5×	body	640	valid
0.0ms	4×	body	1280	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	10	8
2	11	8
done	11	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

13.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify2.5s

Counts

20 → 20

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	33	213
1	89	204
2	226	185
3	515	185
4	1428	185
5	3947	185
done	5000	185

prune55.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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)))

rewrite104.0ms

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` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

75.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
8.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
8.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
9.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
56.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
61.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
57.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.4s

Counts

115 → 115

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	164	2756
1	378	2543
2	1004	2384
3	2844	2129
done	5000	2078

prune314.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

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))))

rewrite127.0ms

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-exp-log` `add-cbrt-cube` `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-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

10.0ms	(+ x (/ (fabs (- y x)) 2.0))
18.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
18.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
76.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ x (/ (fabs (- y x)) 2.0))
49.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
52.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
18.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.6s

Counts

133 → 133

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	135	2667
1	284	1909
2	787	1765
3	2441	1708
done	5000	1674

prune261.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

11.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series732.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (cbrt x) (cbrt x))
179.0ms	(cbrt x)
176.0ms	(cbrt x)
177.0ms	(cbrt x)

simplify3.5s

Counts

93 → 93

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune268.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes73.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8
done	8	8

end0.0ms

sample331.0ms

Algorithm

intervals

Results

140.0ms	7702×	body	80	valid
12.0ms	109×	body	1280	valid
5.0ms	77×	body	640	valid
5.0ms	48×	body	2560	valid
2.0ms	34×	body	320	valid
1.0ms	31×	body	160	valid