Details

analyze3.7s

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

sample272.0ms

Algorithm

intervals

Results

166.0ms	96×	body	1280	valid
58.0ms	59×	body	640	valid
15.0ms	77×	body	80	valid
9.0ms	14×	body	320	valid
4.0ms	10×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	33
1	44	33

prune25.0ms

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

localize32.0ms

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))))))
0.3b	(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 → 57

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)))))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
35.0ms	(* (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))))
48.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4929	1209
1	4929	1209

prune166.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Merged error: 0.1b

Counts

71 → 8

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.5b	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
3.0b	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

4.0ms	(* (sin theta) (sin delta))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
8.0ms	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
4.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
60.0ms	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
57.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4860	1454
1	4860	1454

prune162.0ms

Filtered

62 candidates to 79 candidates (-27.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Merged error: 0.1b

Counts

87 → 9

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.5b	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))))
4.0b	(log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `sin-sum`
7×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `associate--r+` `add-log-exp`
4×	`log-pow`
3×	`exp-prod` `associate-r` `associate-l`
2×	`asin-acos`
1×	`sub-neg` `log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

7.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))))
3.0ms	(log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
44.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))))
5.0ms	(log (exp (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4934	2091
1	4934	2091

prune143.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	78	9	87

Merged error: 0.1b

Counts

87 → 9

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

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)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
6.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
148.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

simplify57.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5029	1397

prune87.0ms

Filtered

37 candidates to 48 candidates (-29.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	47	10	57

Merged error: 0.1b

Counts

57 → 10

regimes603.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	35
1	31	35

end0.0ms

analyze3.5s

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

sample8.9s

Algorithm

intervals

Results

5.7s	3216×	body	1280	valid
1.9s	1842×	body	640	valid
445.0ms	669×	body	320	valid
406.0ms	1976×	body	80	valid
137.0ms	297×	body	160	valid

Details

analyze3.7s

sample272.0ms

simplify3.0ms

prune25.0ms

localize32.0ms

rewrite15.0ms

series98.0ms

simplify69.0ms

prune166.0ms

localize39.0ms

rewrite19.0ms

series131.0ms

simplify46.0ms

prune162.0ms

localize38.0ms

rewrite17.0ms

series92.0ms

simplify76.0ms

prune143.0ms

localize46.0ms

rewrite11.0ms

series164.0ms

simplify57.0ms

prune87.0ms

regimes603.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze3.5s

sample8.9s

Profiling