Details

sample44.0ms

Algorithm

intervals

Results

20.0ms	90×	body	1280	valid
7.0ms	45×	body	640	valid
6.0ms	159×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify62.0ms

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: 30.4b

localize5.0ms

Local error

Found 1 expressions with local error:

4.2b	(- (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)

simplify85.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (79.0ms)

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

prune67.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
12.3b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
13.9b	(* (pow a 2) (pow x 2))
14.4b	(* (pow a 3) (pow x 3))

rewrite26.0ms

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))
12.0ms	(* (pow a 3) (pow x 3))

series304.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
101.0ms	(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))
64.0ms	(* (pow a 3) (pow x 3))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (67.0ms)

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

prune351.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
13.9b	(* (pow a 2) (pow x 2))

rewrite14.0ms

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)) (* a x))
11.0ms	(* (pow a 2) (pow x 2))

series92.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify183.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	188	337
1	727	280
2	4608	269
3	5001	269

prune129.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (fabs (* x a)) (fabs (* x a)))
2.6b	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

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))) (* a x))

series46.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(* (fabs (* x a)) (fabs (* x a)))
39.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

simplify54.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	87	278
1	336	224
2	1512	210
3	5002	204

prune82.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes227.0ms

Accuracy

98% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 21.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	22
1	18	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

582.0ms	2663×	body	1280	valid
204.0ms	1358×	body	640	valid
197.0ms	5464×	body	80	valid
78.0ms	749×	body	320	valid
28.0ms	387×	body	160	valid