Details

sample94.0ms

Algorithm

intervals

Results

60.0ms	93×	body	10240	exit
14.0ms	275×	body	80	valid
2.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	4×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite27.0ms

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` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

5.0ms	(+ 1.0 (exp x))
11.0ms	(- (log (+ 1.0 (exp x))) (* x y))
9.0ms	(log (+ 1.0 (exp x)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ 1.0 (exp x))
95.0ms	(- (log (+ 1.0 (exp x))) (* x y))
91.0ms	(log (+ 1.0 (exp x)))

simplify3.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5026
4	4668
3	1537
2	528
1	211
0	92

prune332.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (- (exp x) 1.0))
0.4b	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
0.5b	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
3.9b	(- (exp x) 1.0)

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`log-prod`
10×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-r`
4×	`associate-/r/`
3×	`associate-/r` `sub-neg` `flip3-+` `associate-l` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `div-exp` `rem-log-exp` `associate-*r/` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

57.0ms	(* (exp x) (- (exp x) 1.0))
122.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
49.0ms	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
14.0ms	(- (exp x) 1.0)

series431.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (exp x) (- (exp x) 1.0))
100.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
256.0ms	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
29.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1420
1	479
0	195

prune859.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1.0 (exp x)))
0.2b	(sqrt (+ 1.0 (exp x)))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

15.0ms	(sqrt (+ 1.0 (exp x)))
15.0ms	(sqrt (+ 1.0 (exp x)))
11.0ms	(log (sqrt (+ 1.0 (exp x))))
11.0ms	(log (sqrt (+ 1.0 (exp x))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ 1.0 (exp x)))
37.0ms	(sqrt (+ 1.0 (exp x)))
133.0ms	(log (sqrt (+ 1.0 (exp x))))
147.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5008
4	3753
3	1118
2	416
1	165
0	86

prune381.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ (/ (* x x) 2) (+ 2.0 x))) (* x y))
0.0b	(+ (/ (* x x) 2) (+ 2.0 x))
6.6b	(log (+ (/ (* x x) 2) (+ 2.0 x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

22.0ms	(- (log (+ (/ (* x x) 2) (+ 2.0 x))) (* x y))
38.0ms	(+ (/ (* x x) 2) (+ 2.0 x))
33.0ms	(log (+ (/ (* x x) 2) (+ 2.0 x)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(- (log (+ (/ (* x x) 2) (+ 2.0 x))) (* x y))
23.0ms	(+ (/ (* x x) 2) (+ 2.0 x))
67.0ms	(log (+ (/ (* x x) 2) (+ 2.0 x)))

simplify1.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	5002
2	1241
1	384
0	138

prune374.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes184.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.1s	2554×	body	10240	exit
705.0ms	8468×	body	80	valid
136.0ms	254×	body	640	valid
86.0ms	120×	body	1280	valid
50.0ms	183×	body	320	valid
13.0ms	93×	body	160	valid