Details

sample95.0ms

Algorithm

intervals

Results

46.0ms	98×	body	1280	valid
24.0ms	71×	body	640	valid
5.0ms	57×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	10×	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: 16.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite17.0ms

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))

series42.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

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

prune108.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.2b

Counts

77 → 8

localize19.0ms

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

rewrite31.0ms

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)))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
51.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5002	1173

prune187.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	96	16	112
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	104	16	120

Merged error: 0.0b

Counts

120 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
10.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune139.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	89	15	104

Merged error: 0.0b

Counts

104 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
82×	`pow1`
65×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
35×	`add-exp-log` `add-cbrt-cube`
34×	`pow-prod-down`
27×	`cos-mult` `sin-mult`
22×	`associate-/r*`
16×	`prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `difference-of-squares`
12×	`associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
7×	`associate-/l*`
6×	`div-inv`
5×	`flip3-+` `frac-add` `flip-+` `sub-div`
4×	`cbrt-undiv` `pow-plus` `div-exp` `add-log-exp`
2×	`pow2` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `*-commutative`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 219

Calls

4 calls:

14.0ms	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
19.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
61.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify60.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	909	5629
1	5001	5076

prune253.0ms

Filtered

166 candidates to 231 candidates (-39.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	230	16	246

Merged error: 0.0b

Counts

246 → 16

regimes332.0ms

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	20	26
1	20	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2931×	body	1280	valid
505.0ms	1877×	body	640	valid
156.0ms	774×	body	320	valid
127.0ms	2068×	body	80	valid
49.0ms	351×	body	160	valid

Details

sample95.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite17.0ms

series42.0ms

simplify38.0ms

prune108.0ms

localize19.0ms

rewrite31.0ms

series104.0ms

simplify53.0ms

prune187.0ms

localize16.0ms

rewrite23.0ms

series85.0ms

simplify47.0ms

prune139.0ms

localize21.0ms

rewrite63.0ms

series157.0ms

simplify60.0ms

prune253.0ms

regimes332.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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