Details

sample294.0ms

Algorithm

intervals

Results

206.0ms	151×	body	1280	valid
52.0ms	59×	body	640	valid
11.0ms	19×	body	320	valid
3.0ms	23×	body	80	valid
1.0ms	4×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	24
1	65	24

prune23.0ms

Filtered

1 candidates to 1 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: 13.5b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (sin phi1) (cos (- lambda1 lambda2)))
2.2b	(sin (- lambda1 lambda2))
2.3b	(cos (- 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×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `sin-diff`

Counts

4 → 60

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
6.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5077	582

prune183.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	14	74

Merged error: 6.9b

Counts

74 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (sin phi1) (cos (- lambda1 lambda2)))
2.3b	(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`cos-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`cos-sum` `associate-*l/`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify37.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5153	811

prune172.0ms

Filtered

57 candidates to 81 candidates (-42.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
9×	`associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
43.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5266	1210

prune167.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	97	13	110

Merged error: 0.0b

Counts

110 → 13

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
0.6b	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
0.6b	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
2.3b	(cos (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3--` `pow1/3` `flip--`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
5.0ms	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
5.0ms	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
4.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
53.0ms	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
57.0ms	(cbrt (* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
4.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5050	922

prune68.0ms

Filtered

43 candidates to 55 candidates (-27.9%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	53	15	68

Merged error: 0.0b

Counts

68 → 15

regimes768.0ms

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	33	38
1	33	38

end0.0ms

sample9.2s

Algorithm

intervals

Results

6.6s	4589×	body	1280	valid
1.7s	1972×	body	640	valid
294.0ms	553×	body	320	valid
110.0ms	700×	body	80	valid
61.0ms	186×	body	160	valid

Details

sample294.0ms

simplify3.0ms

prune23.0ms

localize27.0ms

rewrite20.0ms

series36.0ms

simplify50.0ms

prune183.0ms

localize35.0ms

rewrite21.0ms

series55.0ms

simplify37.0ms

prune172.0ms

localize33.0ms

rewrite30.0ms

series90.0ms

simplify47.0ms

prune167.0ms

localize41.0ms

rewrite20.0ms

series172.0ms

simplify41.0ms

prune68.0ms

regimes768.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.2s

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