Details

sample78.0ms

Algorithm

intervals

Results

36.0ms	89×	body	1280	valid
19.0ms	76×	body	640	valid
7.0ms	57×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	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 (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

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.9b	(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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `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 → 98

Calls

3 calls:

4.0ms	(* r (sin b))
7.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
95.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify45.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	336	803
1	1429	755
2	5002	755

prune260.0ms

Filtered

107 candidates to 81 candidates (75.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	7	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Merged error: 0.2b

Counts

108 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

378×	`add-sqr-sqrt`
244×	`*-un-lft-identity`
173×	`associate-l`
144×	`prod-diff`
132×	`add-cube-cbrt` `times-frac`
117×	`associate-r`
95×	`unswap-sqr`
56×	`distribute-lft-out--` `difference-of-squares`
39×	`*-commutative`
13×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg` `associate-/l*`
11×	`associate-/r*`
8×	`pow1`
6×	`add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv`

Counts

4 → 396

Calls

4 calls:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
23.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
37.0ms	(* r (sin b))
45.0ms	(* (sin a) (sin b))
210.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify139.0ms

Algorithm

egg-herbie

Counts

408 → 408

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1078	7826
1	4131	6379
2	5001	6379

prune822.0ms

Filtered

408 candidates to 188 candidates (46.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	397	11	408
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	404	11	415

Merged error: 0.0b

Counts

415 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

280×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
144×	`prod-diff`
119×	`associate-r`
117×	`associate-l`
115×	`add-cube-cbrt`
67×	`times-frac`
64×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
27×	`*-commutative`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 346

Calls

4 calls:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
31.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))

series529.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
181.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
219.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))

simplify117.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	928	6306
1	3299	4844
2	5001	4649

prune673.0ms

Filtered

358 candidates to 159 candidates (44.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	355	3	358
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	360	9	369

Merged error: 0.0b

Counts

369 → 9

localize15.0ms

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))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

280×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
144×	`prod-diff`
119×	`associate-r`
117×	`associate-l`
115×	`add-cube-cbrt`
67×	`times-frac`
64×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
27×	`*-commutative`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 346

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
24.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
240.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify126.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	924	6407
1	3400	4942
2	5002	4747

prune640.0ms

Filtered

358 candidates to 159 candidates (44.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	355	3	358
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	359	8	367

Merged error: 0.0b

Counts

367 → 8

regimes119.0ms

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	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2763×	body	1280	valid
463.0ms	1820×	body	640	valid
162.0ms	828×	body	320	valid
124.0ms	2251×	body	80	valid
43.0ms	339×	body	160	valid