Details

sample170.0ms

Algorithm

intervals

Results

100.0ms	113×	body	1280	valid
38.0ms	77×	body	640	valid
12.0ms	28×	body	320	valid
4.0ms	16×	body	160	valid
2.0ms	22×	body	80	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

prune3.0ms

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: 0.6b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.1b	(cos (- lambda1 lambda2))
4.4b	(sin (- lambda1 lambda2))

rewrite14.0ms

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×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

Calls

4 calls:

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

series153.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify117.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	205	421
1	508	375
2	1327	374
3	3685	374
4	5002	374

prune223.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	41	11	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	11	53

Merged error: 0.4b

Counts

53 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.1b	(cos (- lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
116.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	255	532
1	758	467
2	2312	466
3	5002	466

prune258.0ms

Filtered

60 candidates to 45 candidates (75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	60	11	71

Merged error: 0.1b

Counts

71 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

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

Counts

4 → 57

Calls

4 calls:

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

series321.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos lambda1) (sin lambda2))
44.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
213.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	309	746
1	1069	642
2	4897	641
3	5001	641

prune266.0ms

Filtered

69 candidates to 49 candidates (71.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 0.1b

Counts

80 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
0.6b	(pow (cos (- lambda1 lambda2)) 3)
4.1b	(cos (- lambda1 lambda2))
4.4b	(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`sub-neg` `cos-sum` `sin-sum`
1×	`+-commutative` `cos-diff` `cube-mult` `pow-to-exp` `pow-pow` `flip3-+` `unpow3` `pow-exp` `sum-log` `sin-diff` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

4.0ms	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
3.0ms	(pow (cos (- lambda1 lambda2)) 3)
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
34.0ms	(pow (cos (- lambda1 lambda2)) 3)
16.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify36.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	258	396
1	981	348
2	5002	343

prune197.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	66	11	77

Merged error: 0.1b

Counts

77 → 11

regimes358.0ms

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	30	22
1	30	22

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.2s	3499×	body	1280	valid
1.2s	2357×	body	640	valid
323.0ms	947×	body	320	valid
104.0ms	450×	body	160	valid
82.0ms	747×	body	80	valid