Details

sample320.0ms

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

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize12.0ms

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))

rewrite41.0ms

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×	`expm1-log1p-u` `associate-l` `clear-num` `log1p-expm1-u` `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 → 84

Calls

3 calls:

26.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series165.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* r (/ (sin b) (cos (+ a b))))
39.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	278	596
1	1172	540
2	5001	540

prune181.0ms

Filtered

93 candidates to 69 candidates (25.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 0.2b

Counts

94 → 8

localize16.0ms

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))))

rewrite77.0ms

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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 187

Calls

4 calls:

5.0ms	(* (cos a) (cos b))
32.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
26.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos a) (cos b))
218.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))
115.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify75.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	560	2080
1	2414	1957
2	5003	1949

prune477.0ms

Filtered

199 candidates to 133 candidates (33.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	189	10	199
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	197	10	207

Merged error: 0.0b

Counts

207 → 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)))))

rewrite98.0ms

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×	`expm1-log1p-u` `div-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `flip3--` `frac-2neg` `1-exp` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 225

Calls

4 calls:

5.0ms	(* (cos a) (cos b))
45.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
31.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
225.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
49.0ms	(* (sin a) (sin b))
119.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	698	2222
1	3297	1979
2	5002	1878

prune546.0ms

Filtered

237 candidates to 153 candidates (35.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	237	10	247

Merged error: 0.0b

Counts

247 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

272×	`add-sqr-sqrt`
189×	`*-un-lft-identity`
138×	`times-frac`
83×	`associate-r`
77×	`associate-l`
76×	`cbrt-prod`
74×	`add-cube-cbrt`
71×	`unswap-sqr`
56×	`distribute-lft-out--` `difference-of-squares`
28×	`add-cbrt-cube`
22×	`add-exp-log` `associate-/r*`
20×	`associate-*r/`
13×	`pow1` `associate-/l*`
11×	`cbrt-unprod`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv`
5×	`pow-prod-down` `cos-mult` `sin-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `clear-num`
2×	`flip3--` `frac-2neg` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 282

Calls

4 calls:

22.0ms	(/ (cbrt 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (cos a) (cos b))
5.0ms	(* (sin a) (sin b))
47.0ms	(* (* (sin b) r) (/ (cbrt 1) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (cbrt 1) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (cos a) (cos b))
45.0ms	(* (sin a) (sin b))
235.0ms	(* (* (sin b) r) (/ (cbrt 1) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	875	3819
1	4123	3574
2	5001	3529

prune714.0ms

Filtered

294 candidates to 187 candidates (36.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	292	2	294
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	294	10	304

Merged error: 0.0b

Counts

304 → 10

regimes154.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	12
1	21	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2892×	body	1280	valid
485.0ms	1882×	body	640	valid
139.0ms	774×	body	320	valid
127.0ms	2125×	body	80	valid
42.0ms	330×	body	160	valid