Details

sample79.0ms

Algorithm

intervals

Results

40.0ms	93×	body	1280	valid
19.0ms	63×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	70×	body	80	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.7b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.7b	(cos (+ a b))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

2×	`cos-sum` `-commutative` `associate-/l`
1×	`+-commutative` `frac-2neg` `clear-num` `div-inv`

Counts

3 → 8

Calls

3 calls:

3.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
5.0ms	(cos (+ a b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
94.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify73.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	81	66
1	169	66
2	501	65
3	1770	64
4	5002	64

prune41.0ms

Filtered

17 candidates to 10 candidates (58.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	12	5	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	5	18

Merged error: 0.3b

Counts

18 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`*-commutative`
2×	`flip3--` `frac-sub` `flip--` `associate-/l*` `sub-div`
1×	`sub-neg` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 18

Calls

4 calls:

2.0ms	(* r (sin b))
7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* r (sin b))
82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms	(* (sin a) (sin b))
213.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	181	253
1	526	251
2	1627	235
3	5001	225

prune100.0ms

Filtered

30 candidates to 22 candidates (73.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	28	7	35

Merged error: 0.1b

Counts

35 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/r/`
7×	`sin-mult`
6×	`cos-mult`
5×	`associate-r`
3×	`flip3--` `associate-r/` `clear-num` `-commutative` `frac-sub` `flip--` `sub-div`
2×	`frac-2neg` `associate-l` `un-div-inv` `div-inv`
1×	`sub-neg` `inv-pow`

Counts

4 → 29

Calls

4 calls:

7.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms	(* (sin a) (sin b))
10.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* (sin a) (sin b))
210.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	203	327
1	700	323
2	3436	292
3	5001	292

prune130.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	39	9	48

Merged error: 0.1b

Counts

48 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/r/`
7×	`sin-mult`
6×	`cos-mult`
5×	`associate-r`
3×	`flip3--` `associate-*r/` `clear-num` `frac-sub` `flip--` `sub-div`
2×	`frac-2neg` `*-commutative` `div-inv`
1×	`sub-neg` `un-div-inv`

Counts

4 → 25

Calls

4 calls:

7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
3.0ms	(* (sin a) (sin b))
9.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
177.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
42.0ms	(* (sin a) (sin b))
226.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	193	310
1	631	308
2	2604	279
3	5002	274

prune100.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	37	9	46

Merged error: 0.1b

Counts

46 → 9

regimes138.0ms

Accuracy

0% (0.2b 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	15	10
1	15	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2932×	body	1280	valid
478.0ms	1830×	body	640	valid
141.0ms	758×	body	320	valid
127.0ms	2147×	body	80	valid
49.0ms	334×	body	160	valid