Details

sample33.0ms

Algorithm

intervals

Results

16.0ms	95×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	23	12
3	27	12
4	29	12
5	34	12
6	36	12
done	36	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

3.0ms	(hypot 1.0 x)
2.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(/ 1.0 (hypot 1.0 x))
71.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
87.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.1s

Counts

73 → 73

Iterations

Useful iterations: 3 (289.0ms)

Iter	Nodes	Cost
0	106	904
1	215	828
2	625	778
3	2020	776
done	5000	776

prune175.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+`

Counts

4 → 79

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series142.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
92.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
38.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.9s

Counts

91 → 91

Iterations

Useful iterations: 3 (410.0ms)

Iter	Nodes	Cost
0	109	1097
1	242	1018
2	862	950
3	3648	943
done	5000	943

prune274.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
11×	`pow1`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `cube-prod`
6×	`sqrt-div` `associate-*r/` `add-log-exp`
5×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `sqrt-pow1`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `pow-prod-down` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow1/3` `diff-log` `pow-exp` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
9.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series350.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
78.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
158.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
37.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify532.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	122	1762
1	311	1370
2	1149	1296
done	5000	1296

prune262.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.1b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`cbrt-prod`
12×	`*-un-lft-identity`
11×	`pow1`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod`
6×	`sqrt-div` `associate-*r/` `add-log-exp`
5×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `sqrt-pow1`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `pow-prod-down` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `pow-exp` `sqrt-pow2` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

8.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
9.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
7.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
94.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
165.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
36.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify3.9s

Counts

96 → 96

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	129	1691
1	306	1307
2	904	1258
3	4887	1254
done	5000	1247

prune215.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

regimes59.0ms

Accuracy

0% (0.0b remaining)

Error of 14.5b against oracle of 14.5b and baseline of 14.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	20	26
done	20	26

end0.0ms

sample856.0ms

Algorithm

intervals

Results

493.0ms	2872×	body	1280	valid
118.0ms	4044×	body	80	valid
91.0ms	621×	body	640	valid
29.0ms	295×	body	320	valid
10.0ms	168×	body	160	valid