Details

sample110.0ms

Algorithm

intervals

Results

38.0ms	89×	body	1280	valid
24.0ms	94×	body	640	valid
17.0ms	278×	body	80	valid
7.0ms	41×	body	320	valid
3.0ms	25×	body	160	valid

simplify372.0ms

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

prune8.0ms

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: 19.7b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
7.3b	(- (exp l) (exp (- l)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

12.0ms	(* J (- (exp l) (exp (- l))))
6.0ms	(- (exp l) (exp (- l)))

series95.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* J (- (exp l) (exp (- l))))
37.0ms	(- (exp l) (exp (- l)))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	260	1031
1	922	661
2	5002	608

prune181.0ms

Filtered

80 candidates to 44 candidates (55.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 0.1b

Counts

81 → 3

localize17.0ms

Local error

Found 4 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)))
0.0b	(* J (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)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 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)))
3.0ms	(* J (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)

series562.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(fma 1/60 (pow l 5) (* 2 l))
59.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
135.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
242.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify112.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	186	510
1	795	442
2	4250	434
3	5001	434

prune238.0ms

Filtered

64 candidates to 49 candidates (76.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Merged error: 0.0b

Counts

67 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (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))))))
2.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
2.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
2.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

345.0ms	(* (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))))))
301.0ms	(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)))))
297.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify134.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	295	1036
1	977	924
2	4587	830
3	5001	830

prune400.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	77	8	85

Merged error: 0.0b

Counts

85 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt J) (cbrt J))
0.6b	(cbrt J)
0.6b	(cbrt J)
0.6b	(cbrt J)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt J) (cbrt J))
1.0ms	(cbrt J)
1.0ms	(cbrt J)
1.0ms	(cbrt J)

series758.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (cbrt J) (cbrt J))
180.0ms	(cbrt J)
184.0ms	(cbrt J)
190.0ms	(cbrt J)

simplify86.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune391.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Merged error: 0.0b

Counts

101 → 8

regimes332.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2654×	body	1280	valid
674.0ms	2580×	body	640	valid
479.0ms	8330×	body	80	valid
254.0ms	1416×	body	320	valid
84.0ms	744×	body	160	valid