Details

sample188.0ms

Algorithm

intervals

Results

109.0ms	122×	body	1280	valid
41.0ms	68×	body	640	valid
10.0ms	28×	body	320	valid
4.0ms	16×	body	160	valid
2.0ms	22×	body	80	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 (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: 0.2b

Counts

2 → 1

localize21.0ms

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))))
3.9b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite17.0ms

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)))))
8.0ms	(+ (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:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify118.0ms

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

prune342.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	43	9	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	9	53

Merged error: 0.1b

Counts

53 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
0.8b	(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
3.9b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series248.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
103.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
17.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify125.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	221	441
1	580	394
2	1497	394
3	4376	394
4	5002	394

prune383.0ms

Filtered

61 candidates to 46 candidates (75.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Merged error: 0.1b

Counts

70 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
0.8b	(log (exp (+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))))
3.9b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

3.0ms	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
6.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series244.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
102.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify131.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	218	489
1	577	427
2	1517	426
3	4486	424
4	5001	424

prune416.0ms

Filtered

59 candidates to 48 candidates (81.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	59	9	68

Merged error: 0.1b

Counts

68 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(log (sqrt (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))))
3.9b	(cos (- lambda1 lambda2))
3.9b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

5.0ms	(log (sqrt (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(log (sqrt (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))))
18.0ms	(cos (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify73.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (20.0ms)

Iter	Nodes	Cost
0	173	475
1	304	430
2	701	427
3	2028	425
4	5001	425

prune423.0ms

Filtered

63 candidates to 49 candidates (77.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	63	9	72

Merged error: 0.1b

Counts

72 → 9

regimes641.0ms

Accuracy

0% (0.2b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	23
1	26	23

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.3s	3545×	body	1280	valid
1.3s	2344×	body	640	valid
348.0ms	964×	body	320	valid
111.0ms	442×	body	160	valid
81.0ms	705×	body	80	valid

Details

sample188.0ms

simplify4.0ms

prune6.0ms

localize21.0ms

rewrite17.0ms

series153.0ms

simplify118.0ms

prune342.0ms

localize25.0ms

rewrite17.0ms

series248.0ms

simplify125.0ms

prune383.0ms

localize28.0ms

rewrite18.0ms

series244.0ms

simplify131.0ms

prune416.0ms

localize28.0ms

rewrite18.0ms

series287.0ms

simplify73.0ms

prune423.0ms

regimes641.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

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