Details

sample55.0ms

Algorithm

intervals

Results

22.0ms	85×	body	1280	valid
10.0ms	179×	body	80	valid
8.0ms	47×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (80.0ms)

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

prune91.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
12.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
14.4b	(* (pow a 2) (pow x 2))
19.0b	(* (pow a 3) (pow x 3))

rewrite28.0ms

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))
14.0ms	(* (pow a 3) (pow x 3))

series303.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
100.0ms	(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))
65.0ms	(* (pow a 3) (pow x 3))

simplify77.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (64.0ms)

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

prune360.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

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)
12.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
14.4b	(* (pow a 2) (pow x 2))

rewrite15.0ms

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))
2.0ms	(pow (* x a) 3)
0.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
9.0ms	(* (pow a 2) (pow x 2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
40.0ms	(pow (* x a) 3)
90.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
35.0ms	(* (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

prune270.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (pow (* x a) 3) (* a x))
0.2b	(* (* x a) (* x a))
0.2b	(pow (* x a) 3)
12.8b	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
19×	`add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down`
9×	`prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `pow-plus` `pow-exp` `fma-udef` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `associate-r` `associate-l` `*-commutative` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
10.0ms	(* (* x a) (* x a))
2.0ms	(pow (* x a) 3)
0.0ms	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
29.0ms	(* (* x a) (* x a))
44.0ms	(pow (* x a) 3)
84.0ms	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	211	351
1	1075	312
2	5001	308

prune177.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes119.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	16
1	22	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

694.0ms	2736×	body	1280	valid
248.0ms	5395×	body	80	valid
225.0ms	1275×	body	640	valid
99.0ms	774×	body	320	valid
35.0ms	389×	body	160	valid