Details

sample321.0ms

Algorithm

intervals

Results

42.0ms	98×	body	1280	valid
14.0ms	55×	body	640	valid
7.0ms	26×	body	320	valid
4.0ms	64×	body	80	valid
2.0ms	13×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

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: 15.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
5.0b	(cos (+ a b))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-*r/` `clear-num`
2×	`cos-sum` `frac-2neg` `div-inv`
1×	`+-commutative` `associate-r` `un-div-inv` `*-commutative`

Counts

3 → 11

Calls

3 calls:

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

series173.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	95	69
1	289	69
2	1263	69
3	5001	67

prune45.0ms

Filtered

20 candidates to 11 candidates (55.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	15	5	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	16	5	21

Merged error: 0.2b

Counts

21 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 31

Calls

4 calls:

7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
3.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
215.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify68.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	211	373
1	676	364
2	2733	338
3	5001	306

prune144.0ms

Filtered

43 candidates to 32 candidates (74.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	35	8	43
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	40	8	48

Merged error: 0.1b

Counts

48 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 12

Calls

4 calls:

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

series467.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
221.0ms	(* r (/ (sin b) (fma (cos b) (cos a) (- (* (sin a) (sin b))))))
46.0ms	(* (sin a) (sin b))
114.0ms	(/ (sin b) (fma (cos b) (cos a) (- (* (sin a) (sin b)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	106	117
1	307	117
2	1245	117
3	5001	114

prune87.0ms

Filtered

24 candidates to 16 candidates (66.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 0.1b

Counts

32 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 13

Calls

4 calls:

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

series455.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
217.0ms	(/ r (/ (fma (cos b) (cos a) (- (* (sin a) (sin b)))) (sin b)))
48.0ms	(* (sin a) (sin b))
106.0ms	(/ (fma (cos b) (cos a) (- (* (sin a) (sin b)))) (sin b))

simplify37.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	113	160
1	299	160
2	983	159
3	5001	153

prune67.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 0.1b

Counts

32 → 8

regimes124.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	20	10
2	20	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2919×	body	1280	valid
482.0ms	1866×	body	640	valid
138.0ms	765×	body	320	valid
122.0ms	2109×	body	80	valid
50.0ms	344×	body	160	valid