Details

sample119.0ms

Algorithm

intervals

Results

48.0ms	98×	body	1280	valid
25.0ms	84×	body	640	valid
17.0ms	250×	body	80	valid
7.0ms	36×	body	320	valid
2.0ms	14×	body	160	valid

simplify376.0ms

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: 16.4b

Counts

2 → 1

localize12.0ms

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)
4.3b	(- (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)))

series267.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* J (- (exp l) (exp (- l))))
165.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
40.0ms	(- (exp l) (exp (- l)))

simplify41.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (32.0ms)

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

prune228.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	2	94

Merged error: 0.1b

Counts

94 → 2

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)

series555.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(fma 1/60 (pow l 5) (* 2 l))
54.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
138.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
240.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify108.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (24.0ms)

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

prune236.0ms

Filtered

64 candidates to 49 candidates (76.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	59	7	66

Merged error: 0.0b

Counts

66 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
0.1b	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
0.1b	(* 1/3 (pow l 3))
6.0b	(* J (* 1/3 (pow l 3)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
13×	`associate-r`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-udef`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `*-commutative` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `fma-def` `distribute-lft-in` `flip3-+` `unpow3` `pow-prod-down` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

6.0ms	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
6.0ms	(* 1/3 (pow l 3))
6.0ms	(* J (* 1/3 (pow l 3)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
250.0ms	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
36.0ms	(* 1/3 (pow l 3))
60.0ms	(* J (* 1/3 (pow l 3)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	359	599
1	1580	520
2	5002	508

prune299.0ms

Filtered

93 candidates to 66 candidates (71.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	93	7	100

Merged error: 0.0b

Counts

100 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

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 (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
1.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
145.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
148.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
147.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

simplify143.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	306	1320
1	970	1218
2	4372	1056
3	5001	1030

prune400.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	93	7	100

Merged error: 0.0b

Counts

100 → 7

regimes248.0ms

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

sample3.5s

Algorithm

intervals

Results

1.3s	2751×	body	1280	valid
783.0ms	2613×	body	640	valid
559.0ms	8347×	body	80	valid
290.0ms	1415×	body	320	valid
100.0ms	703×	body	160	valid