Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	87×	body	1280	valid
4.0ms	46×	body	640	valid
3.0ms	168×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	9×	body	160	valid

simplify58.0ms

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: 30.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.5b	(- (exp (* a x)) 1.0)

rewrite7.0ms

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:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series50.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(exp (* a x))
33.0ms	(- (exp (* a x)) 1.0)

simplify80.0ms

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

prune96.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

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)))
13.1b	(* (pow a 2) (pow x 2))
16.4b	(* (pow a 3) (pow x 3))

rewrite25.0ms

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))
11.0ms	(* (pow a 3) (pow x 3))

series314.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(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)))
31.0ms	(* (pow a 2) (pow x 2))
64.0ms	(* (pow a 3) (pow x 3))

simplify77.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (67.0ms)

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

prune578.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 2 expressions with local error:

5.4b	(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
13.1b	(* (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))

series96.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify181.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (26.0ms)

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

prune139.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(pow (* x a) 2)
5.4b	(fma 1/2 (pow (* x a) 2) (* x a))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `add-exp-log`
3×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
2×	`expm1-log1p-u` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `unpow-prod-down` `pow-prod-down` `prod-exp` `fma-udef` `unpow2` `sqr-pow`

Counts

2 → 30

Calls

2 calls:

2.0ms	(pow (* x a) 2)
0.0ms	(fma 1/2 (pow (* x a) 2) (* x a))

series76.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(pow (* x a) 2)
52.0ms	(fma 1/2 (pow (* x a) 2) (* x a))

simplify59.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	88	138
1	311	120
2	1483	120
3	5001	119

prune65.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes248.0ms

Accuracy

98.7% (0.3b remaining)

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

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	27
1	24	27

end0.0ms

sample932.0ms

Algorithm

intervals

Results

428.0ms	2729×	body	1280	valid
127.0ms	1294×	body	640	valid
112.0ms	5499×	body	80	valid
52.0ms	757×	body	320	valid
17.0ms	395×	body	160	valid