Details

sample77.0ms

Algorithm

intervals

Results

42.0ms	94×	body	1280	valid
15.0ms	63×	body	640	valid
4.0ms	73×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.3b	(cos (+ a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

4.0ms	(* r (sin b))
8.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series167.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
104.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	326	781
1	1400	733
2	5001	732

prune194.0ms

Filtered

101 candidates to 75 candidates (25.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 0.2b

Counts

102 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

245×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
132×	`times-frac`
97×	`associate-l`
67×	`unswap-sqr`
59×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
45×	`associate-r`
15×	`add-exp-log` `*-commutative` `add-cbrt-cube`
12×	`associate-/l*`
11×	`associate-/r*`
10×	`pow1`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down` `cos-mult` `sin-mult`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 229

Calls

4 calls:

4.0ms	(* r (sin b))
5.0ms	(* (cos a) (cos b))
5.0ms	(* (sin a) (sin b))
24.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* r (sin b))
41.0ms	(* (cos a) (cos b))
49.0ms	(* (sin a) (sin b))
226.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify90.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	695	3469
1	3036	3381
2	5002	3381

prune519.0ms

Filtered

241 candidates to 145 candidates (39.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	228	13	241
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	236	13	249

Merged error: 0b

Counts

249 → 13

localize15.0ms

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))))

rewrite67.0ms

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))
28.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
21.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
222.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))
120.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify74.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (54.0ms)

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

prune439.0ms

Filtered

191 candidates to 124 candidates (35.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	193	11	204

Merged error: 0b

Counts

204 → 11

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-sqr-sqrt`
171×	`*-un-lft-identity`
140×	`unswap-sqr`
115×	`times-frac`
80×	`difference-of-squares`
71×	`associate-r`
58×	`add-cube-cbrt`
49×	`associate-l`
48×	`distribute-lft-out--`
38×	`associate-/r*`
29×	`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 → 243

Calls

4 calls:

5.0ms	(* (cos a) (cos b))
47.0ms	(* r (/ (sin b) (- (* 1 (* (cos a) (cos b))) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
30.0ms	(/ (sin b) (- (* 1 (* (cos a) (cos b))) (* (sin a) (sin b))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
239.0ms	(* r (/ (sin b) (- (* 1 (* (cos a) (cos b))) (* (sin a) (sin b)))))
47.0ms	(* (sin a) (sin b))
118.0ms	(/ (sin b) (- (* 1 (* (cos a) (cos b))) (* (sin a) (sin b))))

simplify89.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	727	3229
1	2997	3001
2	5002	2976

prune565.0ms

Filtered

255 candidates to 161 candidates (36.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	253	2	255
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	255	11	266

Merged error: 0b

Counts

266 → 11

regimes160.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	22	11
2	22	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2892×	body	1280	valid
478.0ms	1882×	body	640	valid
140.0ms	774×	body	320	valid
121.0ms	2125×	body	80	valid
48.0ms	330×	body	160	valid