Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	83×	body	1280	valid
4.0ms	41×	body	640	valid
3.0ms	162×	body	80	valid
1.0ms	24×	body	320	valid
1.0ms	20×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3
done	5001	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize5.0ms

Local error

Found 1 expressions with local error:

6.0b	(- (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)

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

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

simplify77.0ms

Counts

31 → 31

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	162	253
1	526	172
2	2608	161
3	5002	125
done	5002	125

prune66.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
14.9b	(* (pow a 2) (pow x 2))
17.3b	(* (pow a 3) (pow x 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
14×	`add-cube-cbrt` `*-un-lft-identity` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 134

Calls

4 calls:

0.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
0.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
20.0ms	(* (pow a 2) (pow x 2))
20.0ms	(* (pow a 3) (pow x 3))

series308.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
106.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
35.0ms	(* (pow a 2) (pow x 2))
61.0ms	(* (pow a 3) (pow x 3))

simplify73.0ms

Counts

146 → 146

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	369	802
1	1845	699
2	5001	656
done	5001	656

prune373.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (pow (* x a) 3) (* a x))
0.2b	(pow (* x a) 3)
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
14.9b	(* (pow a 2) (pow x 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`unswap-sqr`
15×	`unpow-prod-down`
11×	`sqr-pow`
10×	`prod-exp` `unpow2`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r` `associate-l` `pow-exp`
7×	`pow1` `pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `pow-prod-down` `cbrt-unprod` `fma-udef` `rem-cube-cbrt`
1×	`cube-mult` `unpow3` `cube-prod` `*-commutative`

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
6.0ms	(pow (* x a) 3)
0.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
20.0ms	(* (pow a 2) (pow x 2))

series249.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
42.0ms	(pow (* x a) 3)
91.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
32.0ms	(* (pow a 2) (pow x 2))

simplify51.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	278	520
1	1235	418
2	5002	414
done	5002	414

prune271.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (pow (* x a) 3) (* a x))
0.2b	(* (fabs (* x a)) (fabs (* x a)))
0.2b	(pow (* x a) 3)
12.1b	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (fma 1/6 (pow (* x a) 3) (* a x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
11×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `fma-udef` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

0.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
7.0ms	(* (fabs (* x a)) (fabs (* x a)))
9.0ms	(pow (* x a) 3)
0.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (fma 1/6 (pow (* x a) 3) (* a x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
9.0ms	(* (fabs (* x a)) (fabs (* x a)))
42.0ms	(pow (* x a) 3)
106.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (fma 1/6 (pow (* x a) 3) (* a x)))

simplify34.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	183	459
1	797	383
2	5001	369
done	5001	369

prune209.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

96.4% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 21.3b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14
done	18	14

end0.0ms

sample932.0ms

Algorithm

intervals

Results

397.0ms	2708×	body	1280	valid
132.0ms	1401×	body	640	valid
92.0ms	5379×	body	80	valid
44.0ms	713×	body	320	valid
16.0ms	388×	body	160	valid