Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	84×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	157×	body	80	valid
2.0ms	30×	body	320	valid
1.0ms	17×	body	160	valid

simplify59.0ms

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: 30.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (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:

2.0ms	(exp (* a x))
4.0ms	(- (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)

simplify81.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (77.0ms)

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: 8.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
16.2b	(* (pow a 2) (pow x 2))
18.5b	(* (pow a 3) (pow x 3))

rewrite21.0ms

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:

1.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
7.0ms	(* (pow a 2) (pow x 2))
9.0ms	(* (pow a 3) (pow x 3))

series307.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(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))
63.0ms	(* (pow a 3) (pow x 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (64.0ms)

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

prune348.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

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)
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
16.2b	(* (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:

1.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
4.0ms	(pow (* x a) 3)
1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
7.0ms	(* (pow a 2) (pow x 2))

series257.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
40.0ms	(pow (* x a) 3)
94.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
36.0ms	(* (pow a 2) (pow x 2))

simplify50.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

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

prune270.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* x a) 2)
0.2b	(pow (* x a) 3)
5.2b	(fma 1/2 (pow (* x a) 2) (* x a))
12.1b	(fma 1/6 (pow (* x a) 3) (fma 1/2 (pow (* x a) 2) (* x a)))

rewrite13.0ms

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:

7.0ms	(pow (* x a) 2)
4.0ms	(pow (* x a) 3)
1.0ms	(fma 1/2 (pow (* x a) 2) (* x a))
1.0ms	(fma 1/6 (pow (* x a) 3) (fma 1/2 (pow (* x a) 2) (* x a)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (* x a) 2)
45.0ms	(pow (* x a) 3)
52.0ms	(fma 1/2 (pow (* x a) 2) (* x a))
74.0ms	(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

prune174.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes136.0ms

Accuracy

98.9% (0.2b 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	24	19
1	24	19

end0.0ms

sample862.0ms

Algorithm

intervals

Results

393.0ms	2640×	body	1280	valid
125.0ms	1311×	body	640	valid
99.0ms	5430×	body	80	valid
51.0ms	832×	body	320	valid
16.0ms	398×	body	160	valid