Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	70×	body	1280	valid
7.0ms	60×	body	640	valid
4.0ms	174×	body	80	valid
2.0ms	32×	body	320	valid
1.0ms	11×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.0b	(- (exp (* a x)) 1.0)

rewrite10.0ms

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))
7.0ms	(- (exp (* a x)) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
32.0ms	(- (exp (* a x)) 1.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (78.0ms)

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

prune81.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	40	6	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	6	47

Merged error: 10.3b

Counts

47 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
10.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
16.9b	(* (pow a 2) (pow x 2))
18.9b	(* (pow a 3) (pow x 3))

rewrite22.0ms

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))

series309.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(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)))
30.0ms	(* (pow a 2) (pow x 2))
66.0ms	(* (pow a 3) (pow x 3))

simplify77.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (66.0ms)

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

prune312.0ms

Filtered

146 candidates to 81 candidates (55.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	145	7	152

Merged error: 6.3b

Counts

152 → 7

localize12.0ms

Local error

Found 2 expressions with local error:

4.4b	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
16.9b	(* (pow a 2) (pow x 2))

rewrite10.0ms

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:

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

series95.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
32.0ms	(* (pow a 2) (pow x 2))

simplify182.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (25.0ms)

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

prune108.0ms

Filtered

69 candidates to 39 candidates (56.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 0.1b

Counts

76 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(pow (* x a) 2)
4.4b	(fma 1/2 (pow (* x a) 2) (* a x))

rewrite5.0ms

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:

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

series73.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(pow (* x a) 2)
47.0ms	(fma 1/2 (pow (* x a) 2) (* a x))

simplify58.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (55.0ms)

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

prune50.0ms

Filtered

36 candidates to 24 candidates (66.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.1b

Counts

40 → 4

regimes381.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b 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	16	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

495.0ms	2707×	body	1280	valid
154.0ms	1296×	body	640	valid
141.0ms	5508×	body	80	valid
61.0ms	766×	body	320	valid
22.0ms	393×	body	160	valid