Details

sample333.0ms

Algorithm

intervals

Results

42.0ms	94×	body	1280	valid
16.0ms	63×	body	640	valid
4.0ms	73×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify13.0ms

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 (100.0%)

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: 16.8b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.3b	(cos (+ a b))

rewrite40.0ms

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:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	572
1	1143	516
2	5001	513

prune168.0ms

Filtered

87 candidates to 63 candidates (27.6%)

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

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
67×	`times-frac`
47×	`associate-r`
42×	`add-cube-cbrt`
41×	`associate-l`
36×	`unswap-sqr`
32×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`associate-/r/`
7×	`associate-/l*`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down` `clear-num` `*-commutative`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 179

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
26.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
18.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos a) (cos b))
216.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms	(* (sin a) (sin b))
118.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify70.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	539	2036
1	2351	1920
2	5002	1919

prune424.0ms

Filtered

191 candidates to 125 candidates (34.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	181	10	191
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	189	10	199

Merged error: 0.0b

Counts

199 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-sqr-sqrt`
140×	`associate-r`
115×	`*-un-lft-identity`
72×	`times-frac`
54×	`associate-*r/`
47×	`associate-l` `unswap-sqr`
46×	`add-cube-cbrt`
32×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*` `add-cbrt-cube`
15×	`pow1` `prod-exp`
9×	`cbrt-unprod`
8×	`associate-/r/` `associate-/l*`
6×	`pow-prod-down` `un-div-inv`
5×	`cos-mult` `*-commutative` `sin-mult`
4×	`div-exp` `clear-num` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `flip3--` `frac-2neg` `1-exp` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 217

Calls

4 calls:

5.0ms	(* (cos a) (cos b))
42.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
28.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
224.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
48.0ms	(* (sin a) (sin b))
117.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	679	2180
1	3236	1945
2	5002	1848

prune504.0ms

Filtered

229 candidates to 145 candidates (36.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	225	4	229
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	228	11	239

Merged error: 0.0b

Counts

239 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

332×	`add-sqr-sqrt`
276×	`times-frac`
260×	`*-un-lft-identity`
124×	`add-cube-cbrt`
74×	`associate-l`
70×	`unswap-sqr`
68×	`distribute-lft-out--` `difference-of-squares`
43×	`associate-/r*`
25×	`associate-/l*`
21×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/l/`
6×	`associate-r` `div-inv`
5×	`cos-mult` `sin-mult`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
1×	`div-sub`

Counts

4 → 288

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
22.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
5.0ms	(* (sin a) (sin b))
25.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos a) (cos b))
120.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
44.0ms	(* (sin a) (sin b))
234.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify125.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	910	4595
1	3868	4456
2	5002	4441

prune669.0ms

Filtered

300 candidates to 198 candidates (34.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	299	12	311

Merged error: 0b

Counts

311 → 12

regimes192.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2892×	body	1280	valid
492.0ms	1882×	body	640	valid
137.0ms	774×	body	320	valid
134.0ms	2125×	body	80	valid
42.0ms	330×	body	160	valid