Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	97×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	158×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	16×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	109	6
6	256	6
7	719	6
8	2462	6
done	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize5.0ms

Local error

Found 1 expressions with local error:

3.5b	(- (exp (* a x)) 1.0)

rewrite6.0ms

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:

5.0ms

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

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify666.0ms

Counts

31 → 31

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	72	472
1	160	384
2	408	313
3	1503	273
done	5000	273

prune67.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.4b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(* x (+ (* (* 1/2 (pow a 2)) x) a))
5.7b	(* (* 1/2 (pow a 2)) x)
11.6b	(fma (* (pow a 3) (pow x 3)) 1/6 (* x (+ (* (* 1/2 (pow a 2)) x) a)))
17.1b	(* (pow a 3) (pow x 3))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`cube-mult` `unpow3` `associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef`

Counts

4 → 116

Calls

4 calls:

34.0ms	(* x (+ (* (* 1/2 (pow a 2)) x) a))
9.0ms	(* (* 1/2 (pow a 2)) x)
0.0ms	(fma (* (pow a 3) (pow x 3)) 1/6 (* x (+ (* (* 1/2 (pow a 2)) x) a)))
12.0ms	(* (pow a 3) (pow x 3))

series241.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (+ (* (* 1/2 (pow a 2)) x) a))
24.0ms	(* (* 1/2 (pow a 2)) x)
96.0ms	(fma (* (pow a 3) (pow x 3)) 1/6 (* x (+ (* (* 1/2 (pow a 2)) x) a)))
63.0ms	(* (pow a 3) (pow x 3))

simplify935.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (360.0ms)

Iter	Nodes	Cost
0	167	1668
1	422	1470
2	1808	1359
done	5000	1359

prune347.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* x a) 3)
2.4b	(* x (+ (* (* 1/2 (pow a 2)) x) a))
5.7b	(* (* 1/2 (pow a 2)) x)
11.6b	(fma (pow (* x a) 3) 1/6 (* x (+ (* (* 1/2 (pow a 2)) x) a)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (* x a) 3)
34.0ms	(* x (+ (* (* 1/2 (pow a 2)) x) a))
9.0ms	(* (* 1/2 (pow a 2)) x)
0.0ms	(fma (pow (* x a) 3) 1/6 (* x (+ (* (* 1/2 (pow a 2)) x) a)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (* x a) 3)
57.0ms	(* x (+ (* (* 1/2 (pow a 2)) x) a))
24.0ms	(* (* 1/2 (pow a 2)) x)
90.0ms	(fma (pow (* x a) 3) 1/6 (* x (+ (* (* 1/2 (pow a 2)) x) a)))

simplify616.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (165.0ms)

Iter	Nodes	Cost
0	129	1103
1	326	963
2	1333	865
done	5000	865

prune448.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 2)
0.2b	(pow (* x a) 3)
4.0b	(+ (* 1/2 (pow (* a x) 2)) (* a x))
11.6b	(fma (pow (* x a) 3) 1/6 (+ (* 1/2 (pow (* a x) 2)) (* a x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log`
7×	`add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `log1p-expm1-u`
2×	`pow-to-exp` `unpow-prod-down` `pow-prod-down` `prod-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `cube-mult` `fma-def` `flip3-+` `unpow3` `cube-prod` `sum-log` `cbrt-unprod` `flip-+` `fma-udef` `unpow2`

Counts

4 → 68

Calls

4 calls:

2.0ms	(pow (* a x) 2)
2.0ms	(pow (* x a) 3)
4.0ms	(+ (* 1/2 (pow (* a x) 2)) (* a x))
0.0ms	(fma (pow (* x a) 3) 1/6 (+ (* 1/2 (pow (* a x) 2)) (* a x)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (* a x) 2)
41.0ms	(pow (* x a) 3)
62.0ms	(+ (* 1/2 (pow (* a x) 2)) (* a x))
82.0ms	(fma (pow (* x a) 3) 1/6 (+ (* 1/2 (pow (* a x) 2)) (* a x)))

simplify559.0ms

Counts

80 → 80

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	104	900
1	245	764
2	971	696
done	5000	696

prune195.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	37
1	23	37
done	23	37

end0.0ms

sample920.0ms

Algorithm

intervals

Results

426.0ms	2708×	body	1280	valid
131.0ms	1309×	body	640	valid
104.0ms	5401×	body	80	valid
52.0ms	756×	body	320	valid
18.0ms	409×	body	160	valid