Details

sample317.0ms

Algorithm

intervals

Results

40.0ms	89×	body	1280	valid
20.0ms	76×	body	640	valid
6.0ms	57×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify11.0ms

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

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: 16.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

8.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series162.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	268	572
1	1153	516
2	5002	513

prune214.0ms

Filtered

87 candidates to 63 candidates (72.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 0.2b

Counts

88 → 8

localize17.0ms

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
67×	`times-frac`
44×	`associate-r`
42×	`associate-l`
40×	`add-cube-cbrt`
39×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `clear-num` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `*-commutative` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 182

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
20.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
211.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
111.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify75.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	528	2233
1	2293	2108
2	5002	2106

prune567.0ms

Filtered

194 candidates to 129 candidates (66.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	182	12	194
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	190	12	202

Merged error: 0.0b

Counts

202 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
93×	`times-frac`
89×	`unpow-prod-down`
56×	`add-cube-cbrt`
52×	`associate-r`
42×	`associate-l`
41×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/r*`
21×	`add-exp-log` `associate-*r/`
13×	`add-cbrt-cube`
9×	`sqr-pow`
8×	`pow1`
7×	`associate-/l*`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
3×	`clear-num` `cbrt-unprod` `sin-mult`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-prod-down` `pow-exp` `un-div-inv` `cos-mult` `*-commutative` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 212

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms	(* r (/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1)))
7.0ms	(* (sin a) (sin b))
22.0ms	(/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1))

series439.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
210.0ms	(* r (/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1)))
42.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1))

simplify88.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	647	2761
1	2876	2502
2	5003	2475

prune668.0ms

Filtered

224 candidates to 137 candidates (61.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	219	5	224
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	223	13	236

Merged error: 0.0b

Counts

236 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ r (/ (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1) (sin b))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

389×	`add-sqr-sqrt`
372×	`times-frac`
315×	`*-un-lft-identity`
187×	`unpow-prod-down`
171×	`add-cube-cbrt`
75×	`associate-l`
73×	`unswap-sqr`
72×	`distribute-lft-out--` `difference-of-squares`
55×	`associate-/r*`
33×	`associate-/l*`
21×	`add-exp-log` `associate-/r/`
17×	`sqr-pow`
13×	`add-cbrt-cube`
10×	`div-exp`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv`
3×	`frac-2neg` `associate-r` `clear-num` `sin-mult`
2×	`pow-to-exp` `pow-exp` `cos-mult`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `sub-div`

Counts

4 → 354

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
34.0ms	(/ r (/ (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1) (sin b)))
5.0ms	(* (sin a) (sin b))
22.0ms	(/ (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1) (sin b))

series467.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
223.0ms	(/ r (/ (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1) (sin b)))
48.0ms	(* (sin a) (sin b))
114.0ms	(/ (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1) (sin b))

simplify151.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	1091	6268
1	4511	5799
2	5001	5792

prune998.0ms

Filtered

366 candidates to 208 candidates (56.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	361	5	366
Fresh	8	3	11
Picked	0	1	1
Done	0	1	1
Total	369	10	379

Merged error: 0.0b

Counts

379 → 10

regimes145.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2763×	body	1280	valid
477.0ms	1820×	body	640	valid
159.0ms	828×	body	320	valid
130.0ms	2251×	body	80	valid
48.0ms	339×	body	160	valid