Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	96×	body	1280	valid
5.0ms	49×	body	640	valid
3.0ms	169×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	6×	body	160	valid

simplify2.2s

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: 30.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
1.9b	(- (exp (* a x)) 1.0)

rewrite24.0ms

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))
14.0ms	(- (exp (* a x)) 1.0)

series48.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
35.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

46 → 46

Iterations

Useful iterations: done (1.6s)

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

prune101.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.1b	(* 1/6 (pow a 3))
8.9b	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
11.5b	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

rewrite30.0ms

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:

14.0ms	(* 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)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 1/2 (pow a 2))
39.0ms	(* 1/6 (pow a 3))
96.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
60.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

simplify2.3s

Counts

94 → 94

Iterations

Useful iterations: done (2.3s)

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

prune279.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* x (pow a 2)) a)
0.7b	(* x (fma 1/2 (* x (pow a 2)) a))
7.0b	(* 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))

series150.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(fma 1/2 (* x (pow a 2)) a)
61.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
31.0ms	(* x (pow a 2))

simplify1.2s

Counts

70 → 70

Iterations

Useful iterations: done (1.2s)

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

prune146.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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)))
0.7b	(* x (fma 1/2 (* (* a x) (pow a (/ 2 2))) a))

rewrite31.0ms

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

series129.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma 1/2 (* (* a x) (pow a (/ 2 2))) a)
20.0ms	(* (* a x) (pow a (/ 2 2)))
67.0ms	(* x (fma 1/2 (* (* a x) (pow a (/ 2 2))) a))

simplify2.0s

Counts

67 → 67

Iterations

Useful iterations: 3 (899.0ms)

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

prune133.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes163.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.6b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	21	28
done	21	28

end0.0ms

sample993.0ms

Algorithm

intervals

Results

415.0ms	2727×	body	1280	valid
129.0ms	1341×	body	640	valid
107.0ms	5418×	body	80	valid
49.0ms	742×	body	320	valid
19.0ms	390×	body	160	valid