Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	81×	body	1280	valid
5.0ms	142×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	22	12
3	26	12
4	28	12
5	33	12
6	35	12
done	35	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`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

3 → 54

Calls

3 calls:

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

series172.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
88.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.4s

Counts

63 → 63

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	105	855
1	201	779
2	454	735
3	1184	733
4	3788	731
done	5001	731

prune134.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `distribute-lft-out`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.0s

Counts

116 → 116

Iterations

Useful iterations: 3 (893.0ms)

Iter	Nodes	Cost
0	141	2407
1	339	2325
2	1085	2139
3	4518	1938
done	5000	1938

prune308.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b	(/ 1.0 (sqrt (hypot 1.0 x)))
0.2b	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
1.5b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
173×	`*-un-lft-identity`
165×	`add-sqr-sqrt` `add-cube-cbrt`
144×	`sqrt-prod`
28×	`associate-/l*`
16×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `distribute-lft-out`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`flip3--` `associate-/r/` `flip--` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 264

Calls

4 calls:

14.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
10.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
3.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x))))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
36.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
6.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
32.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x))))))

simplify997.0ms

Counts

276 → 276

Iterations

Useful iterations: done (981.0ms)

Iter	Nodes	Cost
0	338	7132
1	796	5966
2	2031	5511
done	5000	5509

prune583.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b	(/ 1.0 (sqrt (hypot 1.0 x)))
0.2b	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
1.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
158×	`*-un-lft-identity`
156×	`add-sqr-sqrt` `add-cube-cbrt`
144×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `associate-*r/` `div-exp` `associate--l+`
3×	`sub-neg`
2×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `clear-num` `frac-sub` `flip--`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `associate-/l/` `distribute-lft-out`

Counts

4 → 244

Calls

4 calls:

2.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
10.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
31.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
6.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
38.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))))

simplify1.0s

Counts

256 → 256

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	327	5715
1	759	4871
2	1808	4496
done	5000	4494

prune512.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.5b

regimes98.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.8b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	22	32
done	22	32

end0.0ms

sample811.0ms

Algorithm

intervals

Results

465.0ms	2868×	body	1280	valid
121.0ms	4056×	body	80	valid
75.0ms	576×	body	640	valid
31.0ms	358×	body	320	valid
8.0ms	142×	body	160	valid