Details

sample392.0ms

Algorithm

intervals

Results

77.0ms	25×	body	2560	valid
33.0ms	55×	body	1280	valid
12.0ms	146×	body	80	valid
9.0ms	27×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	4×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	39	7
2	76	7
3	114	7
4	137	7
5	144	7
6	144	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.4b	(/ 1.0 (* F F))
3.6b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.9b	(tan (* PI l))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`tan-quot` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 77

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(/ 1.0 (* F F))
15.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series246.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
132.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
70.0ms	(tan (* PI l))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	323	443
1	1416	374
2	5001	374

prune214.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
29.9b	(tan (* PI l))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`associate-l`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
13×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`pow1` `cbrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(* PI l)
14.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series259.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
18.0ms	(* PI l)
159.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
63.0ms	(tan (* PI l))

simplify92.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	294	496
1	1023	455
2	3911	454
3	5001	451

prune317.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
29.0b	(cos (* PI l))
29.1b	(sin (* PI l))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
16×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

3.0ms	(* PI l)
7.0ms	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series248.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* PI l)
188.0ms	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
16.0ms	(cos (* PI l))
25.0ms	(sin (* PI l))

simplify45.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	341	430
1	1637	341
2	5001	341

prune233.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(* (cbrt PI) (cbrt PI))
29.1b	(sin (* PI l))
29.3b	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`cbrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
7×	`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 → 65

Calls

4 calls:

0.0ms	(cbrt PI)
6.0ms	(* (cbrt PI) (cbrt PI))
2.0ms	(sin (* PI l))
7.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

series43.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(* (cbrt PI) (cbrt PI))
22.0ms	(sin (* PI l))
21.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

simplify134.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	177	348
1	667	311
2	3382	294
3	5002	286

prune232.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.6b

regimes603.0ms

Accuracy

85.2% (0.7b remaining)

Error of 8.5b against oracle of 7.8b and baseline of 12.4b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	67
1	71	67

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.5s	817×	body	2560	valid
1.1s	1637×	body	1280	valid
326.0ms	976×	body	640	valid
310.0ms	4554×	body	80	valid
83.0ms	382×	body	320	valid
31.0ms	210×	body	160	valid
3.0ms	5×	body	10240	exit