Details

sample43.0ms

Algorithm

intervals

Results

16.0ms	84×	body	1280	valid
6.0ms	49×	body	640	valid
5.0ms	186×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	8×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (exp (* a x)) 1.0)

rewrite16.0ms

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:

15.0ms

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

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

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

simplify4.4s

Counts

31 → 31

Iterations

Useful iterations: 4 (2.5s)

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

prune82.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/6 (pow a 3))
6.9b	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
13.1b	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

25.0ms	(* 1/6 (pow a 3))
1.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
1.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

series247.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 1/6 (pow a 3))
125.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
80.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

simplify2.4s

Counts

62 → 62

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	94	792
1	194	745
2	554	665
3	2812	652
done	5000	639

prune321.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* (* a a) x) a)
0.5b	(* x (fma 1/2 (* (* a a) x) a))
6.0b	(* (* a a) x)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

1.0ms	(fma 1/2 (* (* a a) x) a)
15.0ms	(* x (fma 1/2 (* (* a a) x) a))
39.0ms	(* (* a a) x)

series208.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(fma 1/2 (* (* a a) x) a)
100.0ms	(* x (fma 1/2 (* (* a a) x) a))
34.0ms	(* (* a a) x)

simplify2.2s

Counts

62 → 62

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	78	649
1	169	636
2	523	546
3	1585	546
done	5001	546

prune188.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* a (* a x)) a)
0.1b	(* a (* a x))
0.5b	(* x (fma 1/2 (* a (* a x)) a))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

0.0ms	(fma 1/2 (* a (* a x)) a)
31.0ms	(* a (* a x))
7.0ms	(* x (fma 1/2 (* a (* a x)) a))

series149.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1/2 (* a (* a x)) a)
21.0ms	(* a (* a x))
81.0ms	(* x (fma 1/2 (* a (* a x)) a))

simplify1.6s

Counts

61 → 61

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	77	638
1	170	627
2	527	537
3	1490	537
done	5000	537

prune177.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes105.0ms

Accuracy

96.8% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 21.7b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	33
1	24	33
done	24	33

end0.0ms

sample2.0s

Algorithm

intervals

Results

798.0ms	2746×	body	1280	valid
303.0ms	5371×	body	80	valid
291.0ms	1330×	body	640	valid
131.0ms	749×	body	320	valid
29.0ms	367×	body	160	valid