Details

sample221.0ms

Algorithm

intervals

Results

132.0ms	119×	body	1280	valid
46.0ms	69×	body	640	valid
10.0ms	26×	body	320	valid
8.0ms	14×	body	160	valid
4.0ms	28×	body	80	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune5.0ms

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: 0.8b

Counts

2 → 1

localize25.0ms

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))))
3.6b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite13.0ms

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4947	613
1	4947	613

prune150.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	39	13	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	13	53

Merged error: 0.6b

Counts

53 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.6b	(sin (- 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×	`associate-r` `associate-l`
2×	`associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 49

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
53.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms	(sin (- lambda1 lambda2))

simplify28.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5618	857

prune129.0ms

Filtered

47 candidates to 61 candidates (-29.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	62	12	74

Merged error: 0.1b

Counts

74 → 12

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) (cos lambda2)) (* (sin lambda1) (sin 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` `flip-+` `sin-mult`

Counts

4 → 57

Calls

4 calls:

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

series82.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4961	985
1	4961	985

prune130.0ms

Filtered

50 candidates to 69 candidates (-38.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	70	11	81

Merged error: 0.1b

Counts

81 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

3.6b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite18.0ms

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	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
6.0ms	(cos (- lambda1 lambda2))

series16.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify116.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4733	364
1	4733	364

prune82.0ms

Filtered

40 candidates to 52 candidates (-30.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	52	11	63

Merged error: 0.1b

Counts

63 → 11

regimes600.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	49
1	48	49

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.5s	3582×	body	1280	valid
1.3s	2346×	body	640	valid
347.0ms	924×	body	320	valid
100.0ms	413×	body	160	valid
84.0ms	734×	body	80	valid
1.0ms	1×	body	2560	valid

Details

sample221.0ms

simplify15.0ms

prune5.0ms

localize25.0ms

rewrite13.0ms

series40.0ms

simplify45.0ms

prune150.0ms

localize29.0ms

rewrite15.0ms

series78.0ms

simplify28.0ms

prune129.0ms

localize29.0ms

rewrite15.0ms

series82.0ms

simplify45.0ms

prune130.0ms

localize29.0ms

rewrite18.0ms

series16.0ms

simplify116.0ms

prune82.0ms

regimes600.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.8s

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