Details

sample99.0ms

Algorithm

intervals

Results

58.0ms	102×	body	1280	valid
12.0ms	116×	body	80	valid
10.0ms	21×	body	640	valid
4.0ms	13×	body	320	valid
1.0ms	4×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	90
5	90
4	71
3	55
2	39
1	21
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
2.4b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`sqrt-prod` `difference-of-squares`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l` `distribute-lft-out--`
2×	`distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

3 → 61

Calls

3 calls:

10.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
8.0ms	(/ 1/2 (hypot 1 x))
22.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series126.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
10.0ms	(/ 1/2 (hypot 1 x))
73.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify936.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2000
3	2000
2	712
1	232
0	105

prune247.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
2.0b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `insert-posit16` `distribute-lft-out`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `sqrt-prod` `div-inv` `difference-of-squares`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

4.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
16.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
14.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1/2 (hypot 1 x))
10.0ms	(/ 1/2 (hypot 1 x))
64.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
37.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify961.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	2006
3	2006
2	715
1	232
0	106

prune395.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.1b	(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
2.4b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
10×	`log-prod` `exp-sum`
9×	`times-frac`
8×	`sqrt-prod` `add-log-exp` `difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--`
5×	`pow1`
4×	`exp-prod` `insert-posit16`
3×	`associate-/r` `distribute-lft-out` `associate-/l`
2×	`log-div` `flip3--` `exp-diff` `flip--`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `log-pow` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 86

Calls

4 calls:

12.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
5.0ms	(/ 1/2 (hypot 1 x))
28.0ms	(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
23.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
6.0ms	(/ 1/2 (hypot 1 x))
51.0ms	(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
73.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	2001
4	2001
3	1721
2	742
1	284
0	147

prune369.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.1b	(pow E (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
2.4b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`unpow-prod-up` `log-prod`
9×	`times-frac`
8×	`sqrt-prod` `add-log-exp` `difference-of-squares`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `distribute-lft-out--`
4×	`pow-unpow` `insert-posit16`
3×	`associate-/r` `unpow-prod-down` `distribute-lft-out` `associate-/l`
2×	`log-div` `flip3--` `pow-exp` `flip--` `pow-sub`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `e-exp-1` `clear-num` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-exp` `log-pow` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

12.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
8.0ms	(/ 1/2 (hypot 1 x))
45.0ms	(pow E (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
34.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
6.0ms	(/ 1/2 (hypot 1 x))
357.0ms	(pow E (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
75.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	2011
3	2011
2	1072
1	383
0	162

prune388.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

regimes86.0ms

Accuracy

0% (1.0b remaining)

Error of 15.7b against oracle of 14.7b and baseline of 15.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	2909×	body	1280	valid
377.0ms	4006×	body	80	valid
225.0ms	624×	body	640	valid
79.0ms	307×	body	320	valid
26.0ms	154×	body	160	valid