Details

sample99.0ms

Algorithm

intervals

Results

32.0ms	75×	body	1280	valid
20.0ms	78×	body	640	valid
14.0ms	251×	body	80	valid
8.0ms	45×	body	320	valid
5.0ms	19×	body	160	valid

simplify380.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	44	8
2	91	8
3	195	8
4	332	8
5	652	8
6	1279	8
7	1694	8
8	4978	8
9	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 17.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.6b	(- (exp l) (exp (- l)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
28×	`add-cube-cbrt`
27×	`prod-diff`
20×	`associate-l`
13×	`associate-r`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-log-exp` `unswap-sqr`
4×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `*-commutative` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`diff-log`

Counts

3 → 111

Calls

3 calls:

9.0ms	(* J (- (exp l) (exp (- l))))
13.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
9.0ms	(- (exp l) (exp (- l)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* J (- (exp l) (exp (- l))))
97.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
38.0ms	(- (exp l) (exp (- l)))

simplify52.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	372	1446
1	1440	1025
2	5001	970

prune234.0ms

Filtered

120 candidates to 70 candidates (41.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	3	121

Merged error: 0.1b

Counts

121 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0b	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
0.1b	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-l`
31×	`add-sqr-sqrt`
22×	`fma-def`
21×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
6×	`add-log-exp`
5×	`*-commutative`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-udef` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `flip-+`

Counts

4 → 103

Calls

4 calls:

1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
4.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
16.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
12.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
149.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
265.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
182.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	308	969
1	1381	867
2	5003	867

prune351.0ms

Filtered

115 candidates to 88 candidates (23.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	113	5	118

Merged error: 0.0b

Counts

118 → 5

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(fma (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (* J (cos (/ K 2.0))) U)
0.2b	(* J (cos (/ K 2.0)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
1.0ms	(fma (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (* J (cos (/ K 2.0))) U)
5.0ms	(* J (cos (/ K 2.0)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
149.0ms	(fma (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (* J (cos (/ K 2.0))) U)
48.0ms	(* J (cos (/ K 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	158	350
1	565	305
2	2367	297
3	5002	297

prune172.0ms

Filtered

49 candidates to 39 candidates (20.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	48	6	54

Merged error: 0.0b

Counts

54 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
15.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
15.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
15.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cbrt-prod`
67×	`add-sqr-sqrt`
38×	`associate-l`
36×	`associate-r`
33×	`*-un-lft-identity`
29×	`add-cube-cbrt`
22×	`unswap-sqr`
17×	`swap-sqr`
11×	`pow1`
9×	`pow1/3`
8×	`*-commutative` `add-cbrt-cube`
6×	`add-exp-log`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp`

Counts

4 → 145

Calls

4 calls:

14.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
4.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
4.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
4.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

347.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
308.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
312.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
313.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	380	2543
1	1348	2370
2	5001	2189

prune619.0ms

Filtered

157 candidates to 117 candidates (25.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	157	6	163

Merged error: 0.0b

Counts

163 → 6

regimes222.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2623×	body	1280	valid
717.0ms	2614×	body	640	valid
501.0ms	8516×	body	80	valid
258.0ms	1429×	body	320	valid
98.0ms	775×	body	160	valid