Details

sample72.0ms

Algorithm

intervals

Results

37.0ms	85×	body	10240	exit
12.0ms	265×	body	80	valid
3.0ms	10×	body	640	valid
3.0ms	5×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
1.5b	(log (+ 1.0 (exp x)))

rewrite41.0ms

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:

6.0ms	(+ 1.0 (exp x))
27.0ms	(- (log (+ 1.0 (exp x))) (* x y))
6.0ms	(log (+ 1.0 (exp x)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ 1.0 (exp x))
82.0ms	(- (log (+ 1.0 (exp x))) (* x y))
68.0ms	(log (+ 1.0 (exp x)))

simplify1.5s

Counts

54 → 54

Iterations

Useful iterations: 3 (599.0ms)

Iter	Nodes	Cost
0	92	575
1	211	544
2	643	514
3	3055	508
done	5000	508

prune165.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (log (log (+ 1.0 (exp x))))) (* x y))
0.0b	(log (log (+ 1.0 (exp x))))
0.1b	(exp (log (log (+ 1.0 (exp x)))))
1.5b	(log (+ 1.0 (exp x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

26.0ms	(- (exp (log (log (+ 1.0 (exp x))))) (* x y))
1.0ms	(log (log (+ 1.0 (exp x))))
4.0ms	(exp (log (log (+ 1.0 (exp x)))))
6.0ms	(log (+ 1.0 (exp x)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (exp (log (log (+ 1.0 (exp x))))) (* x y))
191.0ms	(log (log (+ 1.0 (exp x))))
69.0ms	(exp (log (log (+ 1.0 (exp x)))))
63.0ms	(log (+ 1.0 (exp x)))

simplify1.9s

Counts

68 → 68

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	119	816
1	252	701
2	780	649
3	3844	643
done	5001	633

prune544.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (cbrt (pow (log (+ 1.0 (exp x))) 3)) (* x y))
0.7b	(cbrt (pow (log (+ 1.0 (exp x))) 3))
0.7b	(pow (log (+ 1.0 (exp x))) 3)
1.5b	(log (+ 1.0 (exp x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

34.0ms	(- (cbrt (pow (log (+ 1.0 (exp x))) 3)) (* x y))
4.0ms	(cbrt (pow (log (+ 1.0 (exp x))) 3))
6.0ms	(pow (log (+ 1.0 (exp x))) 3)
8.0ms	(log (+ 1.0 (exp x)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (cbrt (pow (log (+ 1.0 (exp x))) 3)) (* x y))
69.0ms	(cbrt (pow (log (+ 1.0 (exp x))) 3))
127.0ms	(pow (log (+ 1.0 (exp x))) 3)
94.0ms	(log (+ 1.0 (exp x)))

simplify1.7s

Counts

87 → 87

Iterations

Useful iterations: 2 (234.0ms)

Iter	Nodes	Cost
0	134	1165
1	364	928
2	1859	844
done	5000	844

prune350.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (log (+ 1.0 (exp x))) (sqrt 3))
0.7b	(cbrt (pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3)))
0.8b	(pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3))
1.5b	(log (+ 1.0 (exp x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`unpow-prod-down`
17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod` `pow-unpow`
9×	`pow1`
8×	`add-exp-log`
6×	`sqrt-prod`
5×	`pow-exp` `sqr-pow`
4×	`log-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp`
2×	`log-div` `pow-pow`
1×	`flip3-+` `pow1/3` `rem-log-exp` `flip-+` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

4.0ms	(pow (log (+ 1.0 (exp x))) (sqrt 3))
11.0ms	(cbrt (pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3)))
7.0ms	(pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3))
11.0ms	(log (+ 1.0 (exp x)))

series2.4s

Counts

4 → 12

Calls

4 calls:

367.0ms	(pow (log (+ 1.0 (exp x))) (sqrt 3))
1.2s	(cbrt (pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3)))
728.0ms	(pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3))
77.0ms	(log (+ 1.0 (exp x)))

simplify1.5s

Counts

95 → 95

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	207	1782
1	599	1660
2	2937	1519
done	5000	1513

prune400.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

regimes74.0ms

Accuracy

75% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 1.5b

bsearch23.0ms

Steps

Iters	Range		Point
2	-3.7438246012323813	-3.309911606533295	-3.3641507308706813

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	53	142
1	70	142
done	70	142

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.8s	2460×	body	10240	exit
935.0ms	8466×	body	80	valid
96.0ms	255×	body	640	valid
78.0ms	109×	body	1280	valid
38.0ms	173×	body	320	valid
16.0ms	115×	body	160	valid