Details

sample123.0ms

Algorithm

intervals

Results

44.0ms	94×	body	1280	valid
26.0ms	90×	body	640	valid
16.0ms	256×	body	80	valid
11.0ms	38×	body	320	valid
4.0ms	26×	body	160	valid

simplify370.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	4980	8
9	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 17.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
6.0b	(- (exp l) (exp (- l)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
1.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
5.0ms	(- (exp l) (exp (- l)))

series259.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* J (- (exp l) (exp (- l))))
169.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
38.0ms	(- (exp l) (exp (- l)))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	318	1176
1	1096	780
2	5001	725

prune241.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	1	94

Merged error: 0.1b

Counts

94 → 1

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

3 → 30

Calls

3 calls:

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

series412.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(fma 1/60 (pow l 5) (* 2 l))
57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
236.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify47.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	111	304
1	337	266
2	1488	258
3	5003	258

prune184.0ms

Filtered

39 candidates to 32 candidates (82.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	6	40

Merged error: 0.0b

Counts

40 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`fma-udef`
1×	`+-commutative` `fma-def` `flip3-+` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 54

Calls

4 calls:

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

series579.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(fma 1/60 (pow l 5) (* 2 l))
240.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
164.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	250	651
1	1078	572
2	5002	556

prune237.0ms

Filtered

66 candidates to 49 candidates (74.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
5.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
4.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
165.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
87.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	288	841
1	1139	734
2	5002	733

prune245.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	6	80

Merged error: 0b

Counts

80 → 6

regimes242.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	2691×	body	1280	valid
809.0ms	2680×	body	640	valid
560.0ms	8424×	body	80	valid
295.0ms	1388×	body	320	valid
112.0ms	784×	body	160	valid