Details

sample35.0ms

Algorithm

intervals

Results

18.0ms	110×	body	1280	valid
4.0ms	37×	body	640	valid
3.0ms	150×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	10×	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: 32.0b

localize7.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (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)

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify82.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (78.0ms)

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

prune66.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
9.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
13.7b	(* (pow a 2) (pow x 2))
15.2b	(* (pow a 3) (pow x 3))

rewrite27.0ms

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)))
9.0ms	(* (pow a 2) (pow x 2))
13.0ms	(* (pow a 3) (pow x 3))

series299.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
99.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
30.0ms	(* (pow a 2) (pow x 2))
61.0ms	(* (pow a 3) (pow x 3))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (64.0ms)

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

prune351.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

localize8.0ms

Local error

Found 2 expressions with local error:

4.0b	(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
13.7b	(* (pow a 2) (pow x 2))

rewrite11.0ms

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))
9.0ms	(* (pow a 2) (pow x 2))

series92.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
34.0ms	(* (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

prune132.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (fabs (* x a)) (fabs (* x a)))
4.0b	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* x a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

3.0ms	(* (fabs (* x a)) (fabs (* x a)))
0.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* x a))

series42.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(* (fabs (* x a)) (fabs (* x a)))
35.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* x a))

simplify54.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	87	278
1	335	224
2	1511	210
3	5001	204

prune80.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes213.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11

end0.0ms

sample926.0ms

Algorithm

intervals

Results

428.0ms	2702×	body	1280	valid
134.0ms	1309×	body	640	valid
109.0ms	5479×	body	80	valid
49.0ms	741×	body	320	valid
20.0ms	438×	body	160	valid