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

sample275.0ms

Algorithm

intervals

Results

152.0ms	86×	body	1280	valid
65.0ms	59×	body	640	valid
16.0ms	21×	body	320	valid
15.0ms	75×	body	80	valid
7.0ms	15×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune26.0ms

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

rewrite18.0ms

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))))))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
35.0ms	(* (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))))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4921	1258
1	4921	1258

prune188.0ms

Filtered

48 candidates to 69 candidates (-43.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	60	9	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Merged error: 0.1b

Counts

71 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta)))))))))
3.1b	(log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta)))))))))
4.0ms	(log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))))))
6.0ms	(asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))))
59.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (log (pow (exp (sin delta)) (* (cos phi1) (cos theta)))))))))
29.0ms	(log (pow (exp (sin delta)) (* (cos phi1) (cos theta))))

simplify32.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4985	1308
1	4985	1308

prune162.0ms

Filtered

53 candidates to 68 candidates (-28.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	68	9	77

Merged error: 0.1b

Counts

77 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (cos theta)))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
4.1b	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite21.0ms

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

series138.0ms

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)))))))))
54.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4801	1503
1	4801	1503

prune172.0ms

Filtered

58 candidates to 79 candidates (-36.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	79	9	88

Merged error: 0.1b

Counts

88 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (cos theta)))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(- (cos delta) (* (log (exp (sin phi1))) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
4.1b	(log (exp (sin phi1)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

6.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
4.0ms	(- (cos delta) (* (log (exp (sin phi1))) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
2.0ms	(log (exp (sin phi1)))

series68.0ms

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)))))
44.0ms	(- (cos delta) (* (log (exp (sin phi1))) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
2.0ms	(log (exp (sin phi1)))

simplify46.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4908	881
1	4908	881

prune90.0ms

Filtered

48 candidates to 65 candidates (-35.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	65	9	74

Merged error: 0.1b

Counts

74 → 9

regimes617.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	57	35
1	57	35

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.5s	3093×	body	1280	valid
1.9s	1831×	body	640	valid
516.0ms	726×	body	320	valid
407.0ms	2028×	body	80	valid
147.0ms	322×	body	160	valid

Details

analyze3.7s

sample275.0ms

simplify24.0ms

prune26.0ms

localize32.0ms

rewrite18.0ms

series104.0ms

simplify61.0ms

prune188.0ms

localize37.0ms

rewrite15.0ms

series143.0ms

simplify32.0ms

prune162.0ms

localize40.0ms

rewrite21.0ms

series138.0ms

simplify43.0ms

prune172.0ms

localize35.0ms

rewrite16.0ms

series68.0ms

simplify46.0ms

prune90.0ms

regimes617.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.9s

Profiling