Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample85.0ms

Algorithm

intervals

Results

44.0ms	94×	body	1280	valid
18.0ms	64×	body	640	valid
5.0ms	23×	body	320	valid
5.0ms	68×	body	80	valid
1.0ms	7×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune11.0ms

Filtered

1 candidates to 1 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: 16.7b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

7.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
4.0ms	(cos (+ a b))

series36.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify73.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5123	439

prune80.0ms

Filtered

43 candidates to 56 candidates (-30.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Merged error: 0.2b

Counts

58 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

4.0ms	(* r (sin b))
4.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
47.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5163	959

prune142.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 0.0b

Counts

93 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 99

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
7.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
6.0ms	(* (sin b) (sin a))

series100.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
49.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
26.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5200	1716

prune294.0ms

Filtered

86 candidates to 111 candidates (-29.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
39×	`times-frac`
37×	`*-un-lft-identity`
36×	`add-cube-cbrt`
28×	`associate-r`
24×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`pow1`
6×	`div-exp` `associate-l` `prod-exp` `associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`
1×	`pow-flip` `un-div-inv` `inv-pow`

Counts

4 → 130

Calls

4 calls:

7.0ms	(* (cos a) (/ (cos b) (sin b)))
4.0ms	(/ (cos b) (sin b))
11.0ms	(* r (/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a))))
8.0ms	(/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (cos a) (/ (cos b) (sin b)))
5.0ms	(/ (cos b) (sin b))
42.0ms	(* r (/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a))))
27.0ms	(/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5419	1857

prune121.0ms

Filtered

95 candidates to 142 candidates (-49.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	143	10	153

Merged error: 0.0b

Counts

153 → 10

regimes246.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample2.5s

Algorithm

intervals

Results

1.4s	2929×	body	1280	valid
522.0ms	1842×	body	640	valid
163.0ms	764×	body	320	valid
158.0ms	2146×	body	80	valid
47.0ms	319×	body	160	valid
1.0ms	2×	body	1280	invalid

Details

analyze1.0s

sample85.0ms

simplify3.0ms

prune11.0ms

localize11.0ms

rewrite17.0ms

series36.0ms

simplify73.0ms

prune80.0ms

localize16.0ms

rewrite25.0ms

series80.0ms

simplify47.0ms

prune142.0ms

localize16.0ms

rewrite32.0ms

series100.0ms

simplify60.0ms

prune294.0ms

localize16.0ms

rewrite34.0ms

series90.0ms

simplify79.0ms

prune121.0ms

regimes246.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0s

sample2.5s

Profiling