Details

analyze2.0s

Algorithm: search

sample205.0ms

Algorithm

intervals

Results

124.0ms	117×	body	1280	valid
46.0ms	79×	body	640	valid
12.0ms	31×	body	320	valid
4.0ms	14×	body	160	valid
2.0ms	15×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 0.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))
3.1b	(sin (- lambda1 lambda2))

rewrite19.0ms

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

series53.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))
6.0ms	(sin (- lambda1 lambda2))

simplify73.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (6.0ms)

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

prune158.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	56	11	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	11	68

Merged error: 0.6b

Counts

68 → 11

localize30.0ms

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 lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))

rewrite17.0ms

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

Counts

4 → 54

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
30.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
26.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify118.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	289	748
1	1037	658
2	4438	658
3	5002	658

prune144.0ms

Filtered

48 candidates to 66 candidates (-37.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 0.1b

Counts

77 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.4b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite18.0ms

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

Counts

4 → 61

Calls

4 calls:

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (sin lambda1) (sin lambda2))
34.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
28.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify47.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	340	888
1	1429	773
2	5002	773

prune137.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	73	11	84

Merged error: 0.1b

Counts

84 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))
3.1b	(sin (- 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	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
6.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series16.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	83	235
1	149	215
2	390	215
3	1141	215
4	5001	212

prune86.0ms

Filtered

40 candidates to 52 candidates (-30.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	52	11	63

Merged error: 0.1b

Counts

63 → 11

regimes667.0ms

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	32	24
1	32	24

end0.0ms

analyze2.0s

Algorithm: search

sample6.0s

Algorithm

intervals

Results

3.6s	3564×	body	1280	valid
1.4s	2392×	body	640	valid
558.0ms	903×	body	320	valid
120.0ms	449×	body	160	valid
96.0ms	692×	body	80	valid

Details

analyze2.0s

sample205.0ms

simplify6.0ms

prune5.0ms

localize22.0ms

rewrite19.0ms

series53.0ms

simplify73.0ms

prune158.0ms

localize30.0ms

rewrite17.0ms

series71.0ms

simplify118.0ms

prune144.0ms

localize34.0ms

rewrite18.0ms

series85.0ms

simplify47.0ms

prune137.0ms

localize31.0ms

rewrite18.0ms

series16.0ms

simplify53.0ms

prune86.0ms

regimes667.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0s

sample6.0s

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