Details

sample134.0ms

Algorithm

intervals

Results

52.0ms	90×	body	1280	valid
27.0ms	77×	body	640	valid
19.0ms	239×	body	80	valid
11.0ms	45×	body	320	valid
6.0ms	33×	body	160	valid

simplify361.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

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)))
4.3b	(- (exp l) (exp (- l)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 96

Calls

3 calls:

26.0ms	(* J (- (exp l) (exp (- l))))
26.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
7.0ms	(- (exp l) (exp (- l)))

series178.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* J (- (exp l) (exp (- l))))
88.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
35.0ms	(- (exp l) (exp (- l)))

simplify48.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	348	1300
1	1396	879
2	5001	825

prune244.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

3.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
7.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series336.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
54.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
156.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	219	575
1	1119	477
2	5001	469

prune219.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.1b	(* 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)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
6.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
3.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
154.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
82.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	219	618
1	920	515
2	5001	514

prune223.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

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)))) (cos (/ K 2.0)))) (cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))))
15.4b	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))
15.4b	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))
15.4b	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))

rewrite25.0ms

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:

8.0ms	(* (cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))))
5.0ms	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))
5.0ms	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))
5.0ms	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))))
294.0ms	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))
304.0ms	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))
295.0ms	(cbrt (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	354	1424
1	1187	1267
2	5001	1166

prune417.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes290.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	2724×	body	1280	valid
989.0ms	2626×	body	640	valid
699.0ms	8291×	body	80	valid
383.0ms	1466×	body	320	valid
138.0ms	794×	body	160	valid