Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	89×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	139×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	13×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
3.9b	(- (exp (* a x)) 1.0)

rewrite18.0ms

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:

4.0ms	(exp (* a x))
13.0ms	(- (exp (* a x)) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164

prune94.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
11.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
16.5b	(* (pow a 2) (pow x 2))
18.8b	(* (pow a 3) (pow x 3))

rewrite44.0ms

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)))
16.0ms	(* (pow a 2) (pow x 2))
18.0ms	(* (pow a 3) (pow x 3))

series308.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
103.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
36.0ms	(* (pow a 2) (pow x 2))
61.0ms	(* (pow a 3) (pow x 3))

simplify72.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (63.0ms)

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

prune361.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize9.0ms

Local error

Found 2 expressions with local error:

3.6b	(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
16.5b	(* (pow a 2) (pow x 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`add-exp-log` `unpow-prod-down`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l`
6×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 63

Calls

2 calls:

0.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
19.0ms	(* (pow a 2) (pow x 2))

series97.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
32.0ms	(* (pow a 2) (pow x 2))

simplify175.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	190	337
1	729	280
2	4610	269
3	5001	269

prune126.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* x a) (* x a))
3.6b	(fma 1/2 (* (* x a) (* x a)) (* x a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
17×	`pow-prod-down`
14×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
4×	`pow-sqr` `pow-prod-up`
2×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `pow-plus` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 46

Calls

2 calls:

28.0ms	(* (* x a) (* x a))
0.0ms	(fma 1/2 (* (* x a) (* x a)) (* x a))

series91.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* (* x a) (* x a))
57.0ms	(fma 1/2 (* (* x a) (* x a)) (* x a))

simplify85.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	130	213
1	590	167
2	3020	154
3	5002	154

prune60.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes235.0ms

Accuracy

98% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	19
1	25	19

end0.0ms

sample943.0ms

Algorithm

intervals

Results

405.0ms	2727×	body	1280	valid
124.0ms	1288×	body	640	valid
97.0ms	5386×	body	80	valid
50.0ms	788×	body	320	valid
19.0ms	399×	body	160	valid