Details

sample75.0ms

Algorithm

intervals

Results

18.0ms	35×	body	1280	valid
14.0ms	250×	body	80	valid
13.0ms	43×	body	640	valid
5.0ms	31×	body	320	valid
5.0ms	99×	body	80	overflowed
1.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize17.0ms

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)))
4.2b	(- (exp l) (exp (- l)))

rewrite60.0ms

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:

24.0ms	(* J (- (exp l) (exp (- l))))
26.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
8.0ms	(- (exp l) (exp (- l)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* J (- (exp l) (exp (- l))))
91.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
40.0ms	(- (exp l) (exp (- l)))

simplify52.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (38.0ms)

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

prune260.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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))))
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)))) (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)))

rewrite18.0ms

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-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-udef`
2×	`*-commutative`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `distribute-lft-in` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 66

Calls

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

series608.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
59.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
242.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
168.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	288	798
1	1356	696
2	5003	696

prune315.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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

rewrite21.0ms

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:

0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
10.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
3.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
251.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
90.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))
167.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

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

prune325.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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

rewrite9.0ms

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:

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

series387.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
234.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
92.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	182	497
1	693	431
2	4875	416
3	5001	416

prune201.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes327.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

655.0ms	1229×	body	1280	valid
502.0ms	8353×	body	80	valid
417.0ms	1404×	body	640	valid
195.0ms	3579×	body	80	overflowed
154.0ms	825×	body	320	valid
54.0ms	465×	body	160	valid