Details

sample276.0ms

Algorithm

intervals

Results

198.0ms	144×	body	1280	valid
44.0ms	63×	body	640	valid
10.0ms	21×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	8×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

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: 13.6b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))
4.1b	(sin (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune177.0ms

Filtered

72 candidates to 51 candidates (29.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	57	15	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Merged error: 7.6b

Counts

73 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series64.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	322	653
1	1423	557
2	5001	557

prune152.0ms

Filtered

82 candidates to 56 candidates (31.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.1b

Counts

97 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`associate-l/` `-commutative` `add-log-exp`
2×	`frac-times` `associate-*r/` `cos-mult` `sin-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

5.0ms	(* (sin phi1) (cos phi2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin phi1) (cos phi2))
31.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
26.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	455	955
1	2058	753
2	5001	753

prune170.0ms

Filtered

101 candidates to 59 candidates (41.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 0.0b

Counts

111 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`associate-*l/` `unswap-sqr`
2×	`sin-mult`
1×	`frac-times` `flip3--` `associate-*r/` `flip--`

Counts

4 → 83

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin phi1) (cos phi2))
7.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin phi1) (cos phi2))
27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
28.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	336	779
1	1425	638
2	5002	638

prune85.0ms

Filtered

95 candidates to 60 candidates (36.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Merged error: 0.0b

Counts

107 → 12

regimes634.0ms

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	35	29
1	35	29

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.2s	4640×	body	1280	valid
1.4s	1906×	body	640	valid
268.0ms	574×	body	320	valid
95.0ms	675×	body	80	valid
66.0ms	205×	body	160	valid

Details

sample276.0ms

simplify8.0ms

prune5.0ms

localize25.0ms

rewrite21.0ms

series48.0ms

simplify104.0ms

prune177.0ms

localize34.0ms

rewrite25.0ms

series64.0ms

simplify42.0ms

prune152.0ms

localize35.0ms

rewrite34.0ms

series91.0ms

simplify59.0ms

prune170.0ms

localize35.0ms

rewrite27.0ms

series72.0ms

simplify44.0ms

prune85.0ms

regimes634.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.5s

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