Details

sample415.0ms

Algorithm

intervals

Results

98.0ms	31×	body	2560	valid
32.0ms	57×	body	1280	valid
7.0ms	25×	body	640	valid
7.0ms	146×	body	80	valid
3.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	41	7
2	82	7
3	122	7
4	147	7
5	157	7
6	159	7
7	159	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.4b	(/ 1.0 (* F F))
4.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.2b	(tan (* PI l))

rewrite24.0ms

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` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 85

Calls

4 calls:

3.0ms	(* PI l)
4.0ms	(/ 1.0 (* F F))
9.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series283.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
26.0ms	(/ 1.0 (* F F))
146.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
90.0ms	(tan (* PI l))

simplify43.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398

prune265.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
30.2b	(tan (* PI l))

rewrite21.0ms

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` `add-cbrt-cube`
10×	`pow1` `sqrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 96

Calls

4 calls:

3.0ms	(* PI l)
4.0ms	(* PI l)
9.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series292.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
20.0ms	(* PI l)
175.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
70.0ms	(tan (* PI l))

simplify101.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	305	522
1	1082	478
2	4101	476
3	5001	475

prune363.0ms

Filtered

108 candidates to 78 candidates (72.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
30.3b	(cos (* PI l))
30.5b	(sin (* PI l))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 61

Calls

4 calls:

4.0ms	(* PI l)
8.0ms	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series279.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
215.0ms	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
18.0ms	(cos (* PI l))
25.0ms	(sin (* PI l))

simplify47.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	356	461
1	1749	372
2	5002	370

prune292.0ms

Filtered

73 candidates to 52 candidates (71.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l))))
0.7b	(/ 1 (/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l)))))
30.3b	(cos (* PI l))
30.5b	(sin (* PI l))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
34×	`add-cbrt-cube`
26×	`div-exp`
20×	`times-frac`
16×	`prod-exp`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-undiv`
8×	`cbrt-unprod`
6×	`associate-/r*` `div-inv`
5×	`pow1` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 99

Calls

4 calls:

8.0ms	(/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l))))
9.0ms	(/ 1 (/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l)))))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series480.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l))))
214.0ms	(/ 1 (/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l)))))
18.0ms	(cos (* PI l))
24.0ms	(sin (* PI l))

simplify67.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	474	1183
1	2536	988
2	5002	957

prune275.0ms

Filtered

111 candidates to 61 candidates (55.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.0b

regimes474.0ms

Accuracy

71.9% (1.0b remaining)

Error of 5.4b against oracle of 4.4b and baseline of 8.1b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	39
1	60	39

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.3s	756×	body	2560	valid
897.0ms	1650×	body	1280	valid
253.0ms	1026×	body	640	valid
206.0ms	4515×	body	80	valid
64.0ms	389×	body	320	valid
26.0ms	218×	body	160	valid
2.0ms	6×	body	10240	exit