Details

sample119.0ms

Algorithm

intervals

Results

62.0ms	75×	body	10240	exit
22.0ms	277×	body	80	valid
4.0ms	3×	body	1280	valid
3.0ms	6×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	19	9
done	19	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.7b	(log (+ 1.0 (exp x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-div` `associate--l+`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

14.0ms	(+ 1.0 (exp x))
26.0ms	(- (log (+ 1.0 (exp x))) (* x y))
12.0ms	(log (+ 1.0 (exp x)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(+ 1.0 (exp x))
99.0ms	(- (log (+ 1.0 (exp x))) (* x y))
92.0ms	(log (+ 1.0 (exp x)))

simplify2.4s

Counts

54 → 54

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	92	575
1	208	544
2	499	514
3	1195	508
4	2600	506
done	5000	506

prune141.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
0.0b	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

35×	`log-prod`
27×	`*-un-lft-identity`
20×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `associate--l+`
9×	`pow1` `associate-+r+`
8×	`log-div` `sqrt-div`
7×	`associate-+l+` `log-pow` `distribute-lft-out` `add-log-exp`
6×	`add-exp-log`
5×	`flip3-+` `flip-+`
4×	`add-cbrt-cube`
2×	`associate--l-` `associate-+l-` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--`

Counts

4 → 94

Calls

4 calls:

17.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
45.0ms	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
210.0ms	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
126.0ms	(log (sqrt (+ 1.0 (exp x))))
113.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.7s

Counts

106 → 106

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	135	1638
1	309	1425
2	737	1316
3	2318	1219
done	5000	1214

prune345.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
7.5b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

13.0ms	(* 1/2 (pow x 2))
25.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
26.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
36.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 1/2 (pow x 2))
81.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
19.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
65.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify2.2s

Counts

83 → 83

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	152	1207
1	372	1093
2	1011	1009
3	3558	985
done	5000	982

prune243.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.8b	(cbrt (pow (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) 3))
0.9b	(pow (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) 3)
7.5b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

32.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
3.0ms	(cbrt (pow (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) 3))
6.0ms	(pow (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) 3)
20.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
71.0ms	(cbrt (pow (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) 3))
163.0ms	(pow (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) 3)
73.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	202	1909
1	546	1676
2	1817	1502
done	5000	1482

prune252.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes47.0ms

Accuracy

83.2% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 1.1b

bsearch53.0ms

Steps

Iters	Range		Point
7	-2.5419562586921644e-05	-4.403108084983288e-07	-9.413547838898711e-06

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	66
1	48	66
done	48	66

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	2330×	body	10240	exit
647.0ms	8407×	body	80	valid
433.0ms	247×	body	640	valid
123.0ms	132×	body	1280	valid
80.0ms	189×	body	320	valid
18.0ms	117×	body	160	valid