Details

sample314.0ms

Algorithm

intervals

Results

42.0ms	93×	body	1280	valid
16.0ms	63×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	70×	body	80	valid
0.0ms	3×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 16.7b

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)))
4.7b	(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))

series168.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (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

prune42.0ms

Filtered

20 candidates to 11 candidates (55.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	16	4	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	4	21

Merged error: 0.3b

Counts

21 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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:

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

series440.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
108.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms	(* (sin a) (sin b))

simplify69.0ms

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

prune133.0ms

Filtered

43 candidates to 32 candidates (74.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	37	6	43
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	41	6	47

Merged error: 0.1b

Counts

47 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.2b	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.2b	(* (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 a) (cos b) (- (* (sin a) (sin b))))
3.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
3.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
3.0ms	(* (sin a) (sin b))

series456.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
211.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
112.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))

simplify43.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	112	117
1	318	117
2	1352	117
3	5002	114

prune84.0ms

Filtered

24 candidates to 16 candidates (66.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	23	7	30

Merged error: 0.1b

Counts

30 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

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:

3.0ms	(* r (sin b))
1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
3.0ms	(* (sin a) (sin b))
4.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* r (sin b))
82.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
47.0ms	(* (sin a) (sin b))
212.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 4 (75.0ms)

Iter	Nodes	Cost
0	101	112
1	222	112
2	704	112
3	2379	110
4	5002	107

prune82.0ms

Filtered

21 candidates to 14 candidates (66.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	22	6	28

Merged error: 0.1b

Counts

28 → 6

regimes95.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2932×	body	1280	valid
472.0ms	1830×	body	640	valid
138.0ms	758×	body	320	valid
127.0ms	2147×	body	80	valid
42.0ms	334×	body	160	valid