Details

sample174.0ms

Algorithm

intervals

Results

109.0ms	121×	body	1280	valid
39.0ms	77×	body	640	valid
6.0ms	20×	body	320	valid
4.0ms	29×	body	80	valid
2.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

prune4.0ms

Filtered

1 candidates to 0 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: 0.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

6.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
98.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify74.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	249	435
1	795	394
2	2920	393
3	5001	393

prune266.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	55	12	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	12	68

Merged error: 0.2b

Counts

68 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
2.8b	(sin (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms	(sin (- lambda1 lambda2))

series343.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (sin lambda2))
59.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
214.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
21.0ms	(sin (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	309	578
1	1149	514
2	5002	513

prune304.0ms

Filtered

76 candidates to 53 candidates (69.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 0.1b

Counts

88 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite19.0ms

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`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `associate-+r+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `sin-mult`

Counts

4 → 63

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
43.0ms	(* (sin lambda1) (sin lambda2))
139.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
213.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	345	962
1	1380	834
2	5001	833

prune316.0ms

Filtered

75 candidates to 52 candidates (69.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	73	13	86

Merged error: 0.1b

Counts

86 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff`
2×	`sin-sum`
1×	`sin-diff`

Counts

4 → 40

Calls

4 calls:

4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series73.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cos (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	83	235
1	149	215
2	390	215
3	1141	215
4	5002	215

prune217.0ms

Filtered

52 candidates to 40 candidates (76.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	52	13	65

Merged error: 0.1b

Counts

65 → 13

regimes428.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	30
1	28	30

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.1s	3521×	body	1280	valid
1.2s	2341×	body	640	valid
342.0ms	976×	body	320	valid
90.0ms	414×	body	160	valid
75.0ms	748×	body	80	valid