Details

sample88.0ms

Algorithm

intervals

Results

26.0ms	85×	body	1280	valid
24.0ms	49×	body	640	valid
9.0ms	195×	body	80	valid
5.0ms	31×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.5s

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: 30.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.4b	(- (exp (* a x)) 1.0)

rewrite29.0ms

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:

9.0ms	(exp (* a x))
18.0ms	(- (exp (* a x)) 1.0)

series73.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
49.0ms	(- (exp (* a x)) 1.0)

simplify2.1s

Counts

46 → 46

Iterations

Useful iterations: done (2.1s)

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

prune166.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.1b	(* 1/6 (pow a 3))
9.6b	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
12.6b	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

rewrite56.0ms

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:

17.0ms	(* 1/2 (pow a 2))
35.0ms	(* 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)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 1/2 (pow a 2))
65.0ms	(* 1/6 (pow a 3))
152.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
77.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

simplify3.6s

Counts

94 → 94

Iterations

Useful iterations: done (3.6s)

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

prune457.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* x (pow a 2)) a)
2.2b	(* x (fma 1/2 (* x (pow a 2)) a))
8.3b	(* x (pow a 2))

rewrite25.0ms

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:

1.0ms	(fma 1/2 (* x (pow a 2)) a)
9.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
12.0ms	(* x (pow a 2))

series224.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(fma 1/2 (* x (pow a 2)) a)
108.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
47.0ms	(* x (pow a 2))

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: done (1.8s)

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

prune204.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* (* a x) a) a)
0.2b	(* (* a x) a)
2.2b	(* x (fma 1/2 (* (* a x) a) a))

rewrite31.0ms

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-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`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

0.0ms	(fma 1/2 (* (* a x) a) a)
22.0ms	(* (* a x) a)
7.0ms	(* x (fma 1/2 (* (* a x) a) a))

series198.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(fma 1/2 (* (* a x) a) a)
35.0ms	(* (* a x) a)
86.0ms	(* x (fma 1/2 (* (* a x) a) a))

simplify1.8s

Counts

61 → 61

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	79	641
1	173	631
2	549	538
3	1661	538
done	5001	538

prune177.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes740.0ms

Accuracy

97.7% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 22.1b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	18	24
done	18	24

end0.0ms

sample1.9s

Algorithm

intervals

Results

857.0ms	2594×	body	1280	valid
305.0ms	1341×	body	640	valid
245.0ms	5585×	body	80	valid
91.0ms	782×	body	320	valid
35.0ms	421×	body	160	valid