Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	80×	body	1280	valid
21.0ms	71×	body	640	valid
15.0ms	282×	body	80	valid
7.0ms	42×	body	320	valid
2.0ms	23×	body	160	valid

simplify375.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	271	9
5	533	9
6	1023	9
7	1395	9
8	4369	9
9	5002	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

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)))
7.1b	(- (exp l) (exp (- l)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
10.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* J (- (exp l) (exp (- l))))
93.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
40.0ms	(- (exp l) (exp (- l)))

simplify37.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	264	566
1	1116	481
2	5002	475

prune184.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
0.0b	(* 2 (* J l))
0.1b	(* (* 2 (* J l)) (cos (/ K 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`associate-r` `associate-l`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 50

Calls

3 calls:

7.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
7.0ms	(* 2 (* J l))
7.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
18.0ms	(* 2 (* J l))
57.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	244	365
1	1034	314
2	5002	314

prune108.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
0.0b	(* 2 (* J (* (cos (* 0.5 K)) l)))
0.1b	(* J (* (cos (* 0.5 K)) l))
0.2b	(* (cos (* 0.5 K)) l)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`associate-r`
3×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

8.0ms	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
8.0ms	(* 2 (* J (* (cos (* 0.5 K)) l)))
5.0ms	(* J (* (cos (* 0.5 K)) l))
5.0ms	(* (cos (* 0.5 K)) l)

series253.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
65.0ms	(* 2 (* J (* (cos (* 0.5 K)) l)))
50.0ms	(* J (* (cos (* 0.5 K)) l))
49.0ms	(* (cos (* 0.5 K)) l)

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	265	514
1	1044	433
2	5002	433

prune183.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

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×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

6.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
150.0ms	(cbrt (cos (/ K 2.0)))
148.0ms	(cbrt (cos (/ K 2.0)))
145.0ms	(cbrt (cos (/ K 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	131	583
1	426	532
2	2037	487
3	5001	482

prune240.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes268.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	6
1	16	6

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	2646×	body	1280	valid
672.0ms	2623×	body	640	valid
448.0ms	8362×	body	80	valid
232.0ms	1391×	body	320	valid
96.0ms	815×	body	160	valid