Details

analyze3.9s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

sample313.0ms

Algorithm

intervals

Results

181.0ms	95×	body	1280	valid
73.0ms	62×	body	640	valid
18.0ms	25×	body	320	valid
15.0ms	67×	body	80	valid
3.0ms	7×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	476	33
1	476	33

prune23.0ms

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: 0.2b

Counts

2 → 2

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
38.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
47.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4924	1258
1	4924	1258

prune176.0ms

Filtered

48 candidates to 69 candidates (-43.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.1b

Counts

71 → 7

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin delta) (* (cos phi1) (cos theta)))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.5b	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
1.9b	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`log-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
7×	`associate--r+`
6×	`unpow-prod-down`
5×	`add-log-exp`
3×	`asin-acos` `rem-log-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-div` `sin-diff` `pow-sub` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `associate-r` `pow-exp` `log-pow` `cos-mult` `-commutative` `flip--` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

6.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
8.0ms	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
6.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
63.0ms	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
55.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4812	1500
1	4812	1500

prune189.0ms

Filtered

57 candidates to 79 candidates (-38.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Merged error: 0.1b

Counts

86 → 8

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`asin-acos`
1×	`sqr-cos-a` `sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

4 → 36

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
7.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
150.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

simplify34.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5318	1401

prune160.0ms

Filtered

37 candidates to 48 candidates (-29.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	47	9	56

Merged error: 0.1b

Counts

56 → 9

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
0.6b	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `asin-acos` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 67

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
4.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
4.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3)

series182.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
45.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3))
47.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
84.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3)

simplify56.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4923	2279
1	4923	2279

prune116.0ms

Filtered

48 candidates to 79 candidates (-64.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	79	9	88

Merged error: 0.1b

Counts

88 → 9

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 (1.0ms)

Iter	Nodes	Cost
0	102	35
1	102	35

end0.0ms

sample9.9s

Algorithm

intervals

Results

6.1s	3239×	body	1280	valid
2.2s	1797×	body	640	valid
543.0ms	707×	body	320	valid
447.0ms	1979×	body	80	valid
135.0ms	278×	body	160	valid

Details

analyze3.9s

sample313.0ms

simplify28.0ms

prune23.0ms

localize38.0ms

rewrite17.0ms

series107.0ms

simplify80.0ms

prune176.0ms

localize40.0ms

rewrite23.0ms

series139.0ms

simplify64.0ms

prune189.0ms

localize46.0ms

rewrite12.0ms

series167.0ms

simplify34.0ms

prune160.0ms

localize38.0ms

rewrite15.0ms

series182.0ms

simplify56.0ms

prune116.0ms

regimes676.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.9s

Profiling