Details

sample81.0ms

Algorithm

intervals

Results

45.0ms	98×	body	1280	valid
14.0ms	55×	body	640	valid
6.0ms	26×	body	320	valid
4.0ms	64×	body	80	valid
2.0ms	13×	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: 15.7b

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)))
5.0b	(cos (+ a b))

rewrite12.0ms

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))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
95.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify77.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 4 (74.0ms)

Iter	Nodes	Cost
0	84	64
1	184	64
2	579	64
3	2052	63
4	5001	61

prune45.0ms

Filtered

17 candidates to 10 candidates (58.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	11	6	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	12	6	18

Merged error: 0.2b

Counts

18 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(- (* (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))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 24

Calls

4 calls:

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

series377.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* r (sin b))
80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
216.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify52.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	202	312
1	590	304
2	1892	289
3	5002	256

prune110.0ms

Filtered

36 candidates to 24 candidates (66.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	34	8	42

Merged error: 0.1b

Counts

42 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`associate-/r/` `sin-mult`
6×	`cos-mult` `*-commutative`
4×	`prod-diff`
3×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `sub-div`
2×	`fma-neg`
1×	`sub-neg` `div-sub` `associate-/r*`

Counts

4 → 33

Calls

4 calls:

7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms	(* (sin a) (sin b))
11.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
8.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))

series498.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
128.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
247.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))

simplify74.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	247	399
1	735	391
2	2636	363
3	5001	363

prune156.0ms

Filtered

45 candidates to 36 candidates (80.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	39	6	45
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	44	9	53

Merged error: 0.1b

Counts

53 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`associate-/l*`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult`

Counts

4 → 9

Calls

4 calls:

2.0ms	(* r (sin b))
1.0ms	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
6.0ms	(* (sin a) (sin b))
3.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin a) (sin b)))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* r (sin b))
82.0ms	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
42.0ms	(* (sin a) (sin b))
211.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin a) (sin b)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 4 (71.0ms)

Iter	Nodes	Cost
0	95	112
1	211	112
2	629	112
3	2073	110
4	5001	107

prune54.0ms

Filtered

21 candidates to 14 candidates (66.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	20	10	30

Merged error: 0.1b

Counts

30 → 10

regimes146.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	20	9
2	20	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2919×	body	1280	valid
479.0ms	1866×	body	640	valid
142.0ms	765×	body	320	valid
128.0ms	2109×	body	80	valid
45.0ms	344×	body	160	valid