Details

sample969.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results

39.0ms	80×	body	1280	valid
17.0ms	60×	body	640	valid
5.0ms	27×	body	320	valid
5.0ms	75×	body	80	valid
2.0ms	14×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 13.8b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series40.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
5.0ms	(cos (+ a b))

simplify37.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune101.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Merged error: 0.2b

Counts

77 → 6

localize15.0ms

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
7.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
51.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune171.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`associate-r`
20×	`times-frac`
14×	`pow1` `prod-exp`
9×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`associate-*r/` `cos-mult` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 118

Calls

4 calls:

11.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
7.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
6.0ms	(* (sin a) (sin b))
12.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
22.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))
27.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	458	1485
1	2012	1270
2	5001	1238

prune149.0ms

Filtered

80 candidates to 130 candidates (-62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Merged error: 0.0b

Counts

143 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r` `add-cbrt-cube`
18×	`times-frac`
13×	`prod-exp`
12×	`pow1`
8×	`associate-/r/`
7×	`cbrt-unprod` `sin-mult`
6×	`div-exp` `cos-mult` `add-log-exp`
4×	`associate-l` `pow-prod-down`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-/r` `frac-sub` `flip--` `associate-/l` `sub-div`
2×	`*-commutative` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-*r/` `clear-num` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
12.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))
49.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	483	1379
1	2301	1192
2	5001	1164

prune93.0ms

Filtered

75 candidates to 122 candidates (-62.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	122	11	133

Merged error: 0.0b

Counts

133 → 11

regimes243.0ms

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

sample3.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results

1.6s	2909×	body	1280	valid
533.0ms	1810×	body	640	valid
163.0ms	782×	body	320	valid
148.0ms	2145×	body	80	valid
53.0ms	354×	body	160	valid

Details

sample969.0ms

simplify6.0ms

prune4.0ms

localize15.0ms

rewrite16.0ms

series40.0ms

simplify37.0ms

prune101.0ms

localize15.0ms

rewrite32.0ms

series103.0ms

simplify56.0ms

prune171.0ms

localize16.0ms

rewrite39.0ms

series108.0ms

simplify58.0ms

prune149.0ms

localize17.0ms

rewrite31.0ms

series96.0ms

simplify62.0ms

prune93.0ms

regimes243.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.7s

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