Details

sample183.0ms

Algorithm

intervals

Results

102.0ms	114×	body	1280	valid
35.0ms	71×	body	640	valid
19.0ms	39×	body	320	valid
3.0ms	25×	body	80	valid
2.0ms	7×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 1.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))
3.2b	(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))
5.0ms	(sin (- lambda1 lambda2))

series375.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
319.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify121.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	205	421
1	508	374
2	1327	374
3	3685	374
4	5001	374

prune360.0ms

Filtered

52 candidates to 42 candidates (19.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	37	15	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	15	53

Merged error: 1.0b

Counts

53 → 15

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.2b	(sin (- lambda1 lambda2))

rewrite20.0ms

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:

6.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms	(sin (- lambda1 lambda2))

series414.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
56.0ms	(* (sin lambda1) (sin lambda2))
266.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
28.0ms	(sin (- lambda1 lambda2))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (8.0ms)

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

prune476.0ms

Filtered

76 candidates to 53 candidates (30.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 0.1b

Counts

91 → 12

localize29.0ms

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

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

Counts

4 → 58

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

series384.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
53.0ms	(* (sin lambda1) (cos lambda2))
54.0ms	(* (sin lambda1) (sin lambda2))
261.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	311	751
1	1012	646
2	4556	646
3	5001	646

prune476.0ms

Filtered

70 candidates to 50 candidates (28.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	70	12	82

Merged error: 0.1b

Counts

82 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
0.7b	(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

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

series359.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
186.0ms	(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
23.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	279	721
1	1021	665
2	5001	659

prune383.0ms

Filtered

80 candidates to 49 candidates (38.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	79	13	92

Merged error: 0.1b

Counts

92 → 13

regimes809.0ms

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

sample5.4s

Algorithm

intervals

Results

3.2s	3477×	body	1280	valid
1.3s	2398×	body	640	valid
328.0ms	949×	body	320	valid
99.0ms	413×	body	160	valid
79.0ms	763×	body	80	valid

Details

sample183.0ms

simplify4.0ms

prune6.0ms

localize26.0ms

rewrite14.0ms

series375.0ms

simplify121.0ms

prune360.0ms

localize29.0ms

rewrite20.0ms

series414.0ms

simplify40.0ms

prune476.0ms

localize29.0ms

rewrite15.0ms

series384.0ms

simplify112.0ms

prune476.0ms

localize24.0ms

rewrite17.0ms

series359.0ms

simplify42.0ms

prune383.0ms

regimes809.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.4s

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