Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	87×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	176×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	16×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	109	6
6	257	6
7	892	6
8	3602	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.8b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify1.0s

Counts

46 → 46

Iterations

Useful iterations: 3 (270.0ms)

Iter	Nodes	Cost
0	79	557
1	171	457
2	503	377
3	2268	328
done	5001	328

prune103.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ 1.0 (exp (* x a))))
0.0b	(exp (* x a))
0.0b	(exp (* 2 (* x a)))
3.8b	(- (exp (* 2 (* x a))) (* 1.0 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `times-frac`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`fma-neg` `prod-diff`
2×	`exp-prod` `flip3--` `exp-to-pow` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 88

Calls

4 calls:

16.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ 1.0 (exp (* x a))))
1.0ms	(exp (* x a))
2.0ms	(exp (* 2 (* x a)))
9.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

series133.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ 1.0 (exp (* x a))))
14.0ms	(exp (* x a))
17.0ms	(exp (* 2 (* x a)))
43.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

simplify2.0s

Counts

100 → 100

Iterations

Useful iterations: 3 (656.0ms)

Iter	Nodes	Cost
0	151	1798
1	373	1730
2	1090	1598
3	4982	1544
done	5000	1544

prune269.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x a))
0.0b	(exp (* 2 (* x a)))
0.2b	(* (* a x) 6)
3.7b	(- (exp (* (* a x) 6)) (pow 1.0 6))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `prod-diff`
19×	`add-cube-cbrt`
10×	`unpow-prod-down` `add-log-exp`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `sqr-pow`
3×	`fma-neg` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

1.0ms	(exp (* x a))
2.0ms	(exp (* 2 (* x a)))
7.0ms	(* (* a x) 6)
8.0ms	(- (exp (* (* a x) 6)) (pow 1.0 6))

series94.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (* x a))
17.0ms	(exp (* 2 (* x a)))
19.0ms	(* (* a x) 6)
48.0ms	(- (exp (* (* a x) 6)) (pow 1.0 6))

simplify603.0ms

Counts

98 → 98

Iterations

Useful iterations: done (600.0ms)

Iter	Nodes	Cost
0	185	1702
1	397	1381
2	1330	1126
done	5000	1103

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 18 (* a a))
0.2b	(pow (* x a) 3)
0.2b	(* 6 (* a x))
21.5b	(fma (* 18 (* a a)) (* x x) (fma 36 (pow (* x a) 3) (* 6 (* a x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `associate-r` `pow-exp` `*-commutative` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

7.0ms	(* 18 (* a a))
2.0ms	(pow (* x a) 3)
6.0ms	(* 6 (* a x))
0.0ms	(fma (* 18 (* a a)) (* x x) (fma 36 (pow (* x a) 3) (* 6 (* a x))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 18 (* a a))
45.0ms	(pow (* x a) 3)
19.0ms	(* 6 (* a x))
101.0ms	(fma (* 18 (* a a)) (* x x) (fma 36 (pow (* x a) 3) (* 6 (* a x))))

simplify473.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	119	856
1	272	767
2	1077	663
done	5001	663

prune357.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

33.7% (14.2b remaining)

Error of 14.4b against oracle of 0.1b and baseline of 21.6b

bsearch350.0ms

Steps

Iters	Range		Point
10	0.0005333266348582408	7738264586.128652	6913276300.677357
7	-4.233477147491156e+82	-6.388473830684138e+80	-1.8775905144238698e+82

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	44	159
1	54	108
done	54	108

end0.0ms

sample956.0ms

Algorithm

intervals

Results

429.0ms	2689×	body	1280	valid
134.0ms	1271×	body	640	valid
120.0ms	5525×	body	80	valid
54.0ms	760×	body	320	valid
21.0ms	433×	body	160	valid