Details

sample52.0ms

Algorithm

intervals

Results

22.0ms	89×	body	1280	valid
5.0ms	36×	body	640	valid
5.0ms	167×	body	80	valid
3.0ms	26×	body	320	valid
0.0ms	6×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	116	6
6	273	6
7	807	6
8	2954	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.1b	(- (exp (* a x)) 1.0)

rewrite26.0ms

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:

8.0ms	(exp (* a x))
16.0ms	(- (exp (* a x)) 1.0)

series70.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(exp (* a x))
50.0ms	(- (exp (* a x)) 1.0)

simplify2.4s

Counts

46 → 46

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	79	557
1	175	457
2	393	386
3	1277	346
done	5000	316

prune163.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(exp (* 2 (* a x)))
2.1b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
103×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
87×	`unpow-prod-down` `cube-prod`
79×	`add-cube-cbrt`
33×	`sqr-pow`
25×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`fma-neg` `add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 228

Calls

4 calls:

5.0ms	(exp (* a x))
4.0ms	(exp (* a x))
9.0ms	(exp (* 2 (* a x)))
67.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series166.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(exp (* a x))
14.0ms	(exp (* a x))
29.0ms	(exp (* 2 (* a x)))
109.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify1.7s

Counts

240 → 240

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	233	7343
1	517	4062
2	1294	3105
done	5000	2504

prune431.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (* a x))
4.8b	(* (pow x 3) a)
13.3b	(* (pow a 2) (+ (pow x 2) (* (pow x 3) a)))
13.5b	(+ (pow x 2) (* (pow x 3) a))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`associate-l`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`unpow-prod-down`
9×	`pow1` `prod-exp`
8×	`fma-def` `unswap-sqr`
7×	`associate-r`
6×	`add-log-exp`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u`
3×	`pow-prod-down` `*-commutative` `unpow2`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `sum-log`

Counts

4 → 107

Calls

4 calls:

38.0ms	(* 3 (* a x))
13.0ms	(* (pow x 3) a)
66.0ms	(* (pow a 2) (+ (pow x 2) (* (pow x 3) a)))
14.0ms	(+ (pow x 2) (* (pow x 3) a))

series233.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 3 (* a x))
26.0ms	(* (pow x 3) a)
125.0ms	(* (pow a 2) (+ (pow x 2) (* (pow x 3) a)))
56.0ms	(+ (pow x 2) (* (pow x 3) a))

simplify1.8s

Counts

119 → 119

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	151	1302
1	397	1192
2	1502	1029
done	5000	1024

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x x (* (pow x 3) a))
2.9b	(* (pow a (/ 2 2)) (* (fma x x (* (pow x 3) a)) a))
4.8b	(* (pow x 3) a)
6.9b	(* (fma x x (* (pow x 3) a)) a)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
22×	`associate-l`
21×	`add-sqr-sqrt`
13×	`prod-exp` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down` `associate-r`
6×	`pow1`
5×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `*-commutative` `sqr-pow`
1×	`cube-mult` `unpow3` `pow-prod-down` `fma-udef`

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma x x (* (pow x 3) a))
44.0ms	(* (pow a (/ 2 2)) (* (fma x x (* (pow x 3) a)) a))
29.0ms	(* (pow x 3) a)
16.0ms	(* (fma x x (* (pow x 3) a)) a)

series369.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma x x (* (pow x 3) a))
182.0ms	(* (pow a (/ 2 2)) (* (fma x x (* (pow x 3) a)) a))
31.0ms	(* (pow x 3) a)
98.0ms	(* (fma x x (* (pow x 3) a)) a)

simplify5.4s

Counts

101 → 101

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	126	1289
1	283	1159
2	932	986
3	4880	961
done	5000	957

prune632.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

96.9% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 21.4b

bsearch2.0ms

simplify12.0ms

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	26	60
1	32	58
2	33	56
done	33	56

end0.0ms

sample2.3s

Algorithm

intervals

Results

817.0ms	2705×	body	1280	valid
677.0ms	5432×	body	80	valid
261.0ms	1331×	body	640	valid
88.0ms	787×	body	320	valid
59.0ms	372×	body	160	valid