Details

sample76.0ms

Algorithm

intervals

Results

36.0ms	90×	body	1280	valid
9.0ms	127×	body	80	valid
7.0ms	23×	body	640	valid
3.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite49.0ms

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:

10.0ms	(/ 1.0 (hypot 1.0 x))
23.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series316.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1.0 (hypot 1.0 x))
134.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
167.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.3s

Counts

63 → 63

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	105	855
1	217	779
2	717	735
3	4244	733
done	5000	733

prune390.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.5b

localize39.0ms

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)))))
0.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite72.0ms

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` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+`

Counts

4 → 81

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ 1.0 (hypot 1.0 x))
31.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
17.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(/ 1.0 (hypot 1.0 x))
134.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
57.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	112	1111
1	276	1032
2	1324	964
done	5001	959

prune659.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(exp (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`log-div` `exp-prod` `add-cbrt-cube`
3×	`flip3--` `exp-sum` `flip--`
2×	`sqrt-pow1` `exp-diff` `sqrt-div` `associate-*r/` `log-pow` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow1/2` `diff-log` `rem-log-exp` `pow-prod-down` `sqrt-prod` `flip-+` `rem-exp-log`

Counts

4 → 58

Calls

4 calls:

24.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
29.0ms	(log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
23.0ms	(exp (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
17.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
178.0ms	(log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
64.0ms	(exp (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
59.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	104	1372
1	235	1258
2	1113	1082
done	5001	1067

prune517.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 16.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (cbrt (pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)))
0.5b	(cbrt (pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))
0.5b	(pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
0.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
17×	`exp-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`pow1`
7×	`add-log-exp`
6×	`log-pow`
5×	`add-exp-log` `add-cbrt-cube`
3×	`cube-mult` `pow-unpow` `unpow3` `sqr-pow`
2×	`associate--r+`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `pow1/3` `diff-log` `pow-exp` `flip--` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 87

Calls

4 calls:

26.0ms	(exp (cbrt (pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)))
7.0ms	(cbrt (pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))
14.0ms	(pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
19.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(exp (cbrt (pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)))
170.0ms	(cbrt (pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))
247.0ms	(pow (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
69.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.6s

Counts

99 → 99

Iterations

Useful iterations: 2 (305.0ms)

Iter	Nodes	Cost
0	103	2185
1	267	1932
2	1375	1580
done	5000	1580

prune594.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 16.5b

regimes344.0ms

Accuracy

0% (0.0b remaining)

Error of 15.0b against oracle of 15.0b and baseline of 15.0b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	28
1	17	28
done	17	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	2806×	body	1280	valid
978.0ms	681×	body	640	valid
347.0ms	4080×	body	80	valid
64.0ms	305×	body	320	valid
17.0ms	128×	body	160	valid