Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	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

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	7

prune8.0ms

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))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

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

simplify1.6s

Counts

20 → 20

Iterations

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

prune127.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

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)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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:

16.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.3s

Counts

4 → 12

Calls

4 calls:

345.0ms	(* (cbrt x) (cbrt x))
307.0ms	(cbrt x)
307.0ms	(cbrt x)
299.0ms	(cbrt x)

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	725
1	142
0	65

prune518.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

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×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

143.0ms	(* (cbrt (+ (/ (fabs (- y x)) 2.0) x)) (cbrt (+ (/ (fabs (- y x)) 2.0) x)))
9.0ms	(cbrt (+ (/ (fabs (- y x)) 2.0) x))
9.0ms	(cbrt (+ (/ (fabs (- y x)) 2.0) x))
12.0ms	(cbrt (+ (/ (fabs (- y x)) 2.0) x))

series388.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (+ (/ (fabs (- y x)) 2.0) x)) (cbrt (+ (/ (fabs (- y x)) 2.0) x)))
86.0ms	(cbrt (+ (/ (fabs (- y x)) 2.0) x))
100.0ms	(cbrt (+ (/ (fabs (- y x)) 2.0) x))
82.0ms	(cbrt (+ (/ (fabs (- y x)) 2.0) x))

simplify925.0ms

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1797
1	450
0	179

prune848.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
30×	`sqrt-prod`
27×	`add-cube-cbrt`
26×	`fma-def`
20×	`pow1`
19×	`times-frac`
14×	`sqrt-div`
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×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `sum-log` `associate-l/` `associate-r/` `hypot-def` `div-inv`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 138

Calls

4 calls:

29.0ms	(sqrt (+ (/ (fabs (- y x)) 2.0) x))
14.0ms	(+ (/ (fabs (- y x)) 2.0) x)
21.0ms	(+ (/ (fabs (- y x)) 2.0) x)
128.0ms	(* (sqrt (+ (/ (fabs (- y x)) 2.0) x)) (sqrt (+ (/ (fabs (- y x)) 2.0) x)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ (/ (fabs (- y x)) 2.0) x))
48.0ms	(+ (/ (fabs (- y x)) 2.0) x)
49.0ms	(+ (/ (fabs (- y x)) 2.0) x)
51.0ms	(* (sqrt (+ (/ (fabs (- y x)) 2.0) x)) (sqrt (+ (/ (fabs (- y x)) 2.0) x)))

simplify1.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	1386
1	318
0	135

prune735.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes163.0ms

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

sample689.0ms

Algorithm

intervals

Results

326.0ms	7662×	body	80	valid
59.0ms	108×	body	1280	valid
13.0ms	67×	body	2560	valid
11.0ms	85×	body	640	valid
5.0ms	50×	body	320	valid
2.0ms	28×	body	160	valid