Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	85×	body	1280	valid
5.0ms	48×	body	640	valid
3.0ms	168×	body	80	valid
2.0ms	30×	body	320	valid
0.0ms	7×	body	160	valid

simplify61.0ms

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: 31.4b

localize5.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (exp (* a x)) 1.0)

rewrite15.0ms

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:

14.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify78.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (75.0ms)

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

prune77.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
11.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
12.0b	(* (pow a 2) (pow x 2))
14.7b	(* (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)))
17.0ms	(* (pow a 2) (pow x 2))
23.0ms	(* (pow a 3) (pow x 3))

series283.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
92.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
28.0ms	(* (pow a 2) (pow x 2))
59.0ms	(* (pow a 3) (pow x 3))

simplify75.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (65.0ms)

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

prune510.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.1b

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)
11.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
12.0b	(* (pow a 2) (pow x 2))

rewrite31.0ms

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))
10.0ms	(pow (* x a) 3)
0.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
17.0ms	(* (pow a 2) (pow x 2))

series227.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
37.0ms	(pow (* x a) 3)
84.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
29.0ms	(* (pow a 2) (pow x 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (43.0ms)

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

prune386.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* x a) 2)
0.2b	(pow (* x a) 3)
4.0b	(fma 1/2 (pow (* x a) 2) (* x a))
11.8b	(fma 1/6 (pow (* x a) 3) (fma 1/2 (pow (* x a) 2) (* x a)))

rewrite17.0ms

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`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `pow-prod-down` `prod-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`
1×	`cube-mult` `unpow3` `cube-prod` `cbrt-unprod` `unpow2`

Counts

4 → 64

Calls

4 calls:

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

series181.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (* x a) 2)
37.0ms	(pow (* x a) 3)
49.0ms	(fma 1/2 (pow (* x a) 2) (* x a))
68.0ms	(fma 1/6 (pow (* x a) 3) (fma 1/2 (pow (* x a) 2) (* x a)))

simplify34.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	171	316
1	768	281
2	5001	281

prune272.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

98.7% (0.3b remaining)

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

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	11

end0.0ms

sample904.0ms

Algorithm

intervals

Results

421.0ms	2715×	body	1280	valid
142.0ms	1364×	body	640	valid
102.0ms	5523×	body	80	valid
46.0ms	725×	body	320	valid
17.0ms	389×	body	160	valid