Details

sample294.0ms

Algorithm

intervals

Results

180.0ms	103×	body	1280	valid
56.0ms	55×	body	640	valid
18.0ms	27×	body	320	valid
12.0ms	64×	body	80	valid
3.0ms	7×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	56	22
2	59	22
3	59	22

prune11.0ms

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: 0.2b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

4.0ms	(* (sin theta) (sin delta))
5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
34.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
45.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	289	930
1	894	837
2	3513	835
3	5002	835

prune155.0ms

Filtered

51 candidates to 70 candidates (-37.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.1b

Counts

71 → 7

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`asin-acos` `pow-unpow`
2×	`pow-pow` `pow-exp` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult` `sqr-pow`

Counts

4 → 47

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series79.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
64.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify159.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	178	844
1	668	728
2	4077	727
3	5002	727

prune172.0ms

Filtered

44 candidates to 59 candidates (-34.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	57	9	66

Merged error: 0.1b

Counts

66 → 9

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos delta) 3)
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `unpow-prod-down` `pow-unpow` `cube-prod` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cube-div`
2×	`cube-mult` `pow-to-exp` `asin-acos` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`flip3-+` `associate-*r/` `frac-add` `cos-mult` `sin-cos-mult` `flip-+`

Counts

4 → 65

Calls

4 calls:

2.0ms	(pow (cos delta) 3)
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

series63.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos delta) 3)
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
48.0ms	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

simplify57.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	349	825
1	1616	716
2	5002	707

prune200.0ms

Filtered

47 candidates to 77 candidates (-63.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
0.6b	(pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3) 3)
5.9b	(cbrt (pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3) 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

39×	`unpow-prod-down` `cube-prod`
30×	`cbrt-prod`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`cube-div`
7×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
6×	`pow-unpow` `add-cbrt-cube`
5×	`pow1` `pow-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `cbrt-div` `flip3-+` `associate-*r/` `frac-add` `cos-mult` `sin-cos-mult` `flip-+`
2×	`pow-pow` `rem-cube-cbrt`
1×	`asin-acos` `pow1/3` `rem-cbrt-cube`

Counts

4 → 122

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
10.0ms	(pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3) 3)
10.0ms	(cbrt (pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3) 3))

series290.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
45.0ms	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
194.0ms	(pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3) 3)
45.0ms	(cbrt (pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	467	2229
1	1998	2012
2	5001	1984

prune181.0ms

Filtered

59 candidates to 134 candidates (-127.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	134	10	144

Merged error: 0.1b

Counts

144 → 10

regimes676.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	59
1	52	59

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.5s	3119×	body	1280	valid
1.9s	1827×	body	640	valid
545.0ms	2049×	body	80	valid
480.0ms	687×	body	320	valid
145.0ms	318×	body	160	valid

Details

sample294.0ms

simplify6.0ms

prune11.0ms

localize34.0ms

rewrite15.0ms

series94.0ms

simplify90.0ms

prune155.0ms

localize44.0ms

rewrite12.0ms

series79.0ms

simplify159.0ms

prune172.0ms

localize49.0ms

rewrite15.0ms

series63.0ms

simplify57.0ms

prune200.0ms

localize54.0ms

rewrite39.0ms

series290.0ms

simplify80.0ms

prune181.0ms

regimes676.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.0s

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