Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	86×	body	1280	valid
4.0ms	47×	body	640	valid
3.0ms	169×	body	80	valid
1.0ms	24×	body	320	valid
0.0ms	10×	body	160	valid

simplify2.3s

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: 30.5b

localize5.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (exp (* a x)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

14.0ms

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

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify2.8s

Counts

31 → 31

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	72	472
1	164	384
2	369	313
3	1232	255
4	4654	245
done	5000	245

prune65.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.3b	(* 1/6 (pow a 3))
8.8b	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
14.2b	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unpow2`
1×	`cube-mult` `unpow3`

Counts

4 → 82

Calls

4 calls:

12.0ms	(* 1/2 (pow a 2))
13.0ms	(* 1/6 (pow a 3))
0.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
0.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/2 (pow a 2))
36.0ms	(* 1/6 (pow a 3))
92.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
63.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

simplify2.2s

Counts

94 → 94

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	137	1036
1	282	962
2	737	846
3	3838	827
done	5001	814

prune262.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* x (pow a 2)) a)
1.7b	(* x (fma 1/2 (* x (pow a 2)) a))
7.1b	(* x (pow a 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`associate-l`
5×	`pow1` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `pow-exp`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma 1/2 (* x (pow a 2)) a)
7.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
12.0ms	(* x (pow a 2))

series147.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma 1/2 (* x (pow a 2)) a)
63.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
27.0ms	(* x (pow a 2))

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	92	716
1	186	685
2	462	592
3	1604	592
done	5001	589

prune148.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* (* a x) (pow a (/ 2 2))) a)
0.1b	(* (* a x) (pow a (/ 2 2)))
1.7b	(* x (fma 1/2 (* (* a x) (pow a (/ 2 2))) a))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
10×	`associate-r` `prod-exp` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-l` `cbrt-unprod`
3×	`expm1-log1p-u` `unpow-prod-down` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `unswap-sqr` `sqr-pow`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 1/2 (* (* a x) (pow a (/ 2 2))) a)
24.0ms	(* (* a x) (pow a (/ 2 2)))
7.0ms	(* x (fma 1/2 (* (* a x) (pow a (/ 2 2))) a))

series124.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma 1/2 (* (* a x) (pow a (/ 2 2))) a)
21.0ms	(* (* a x) (pow a (/ 2 2)))
61.0ms	(* x (fma 1/2 (* (* a x) (pow a (/ 2 2))) a))

simplify1.9s

Counts

67 → 67

Iterations

Useful iterations: 3 (829.0ms)

Iter	Nodes	Cost
0	100	976
1	230	798
2	668	576
3	2620	573
done	5000	573

prune123.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes213.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.9b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	22	29
done	22	29

end0.0ms

sample915.0ms

Algorithm

intervals

Results

395.0ms	2660×	body	1280	valid
128.0ms	1342×	body	640	valid
96.0ms	5388×	body	80	valid
47.0ms	746×	body	320	valid
17.0ms	425×	body	160	valid