Details

sample258.0ms

Algorithm

intervals

Results

178.0ms	141×	body	1280	valid
47.0ms	63×	body	640	valid
13.0ms	29×	body	320	valid
2.0ms	17×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

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 (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: 13.2b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))
2.7b	(sin (- lambda1 lambda2))

rewrite23.0ms

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

series193.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

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

prune326.0ms

Filtered

72 candidates to 51 candidates (70.8%)

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: 6.7b

Counts

73 → 15

localize37.0ms

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))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite24.0ms

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))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series284.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (cos phi2))
129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

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

prune408.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	84	13	97

Merged error: 0.1b

Counts

97 → 13

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
127.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
48.0ms	(* (sin lambda1) (sin lambda2))
112.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	433	949
1	2002	747
2	5001	747

prune462.0ms

Filtered

101 candidates to 59 candidates (58.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	99	15	114

Merged error: 0.0b

Counts

114 → 15

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

9.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
131.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms	(* (sin lambda1) (sin lambda2))
112.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	448	907
1	2047	720
2	5001	720

prune386.0ms

Filtered

98 candidates to 61 candidates (62.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	98	15	113

Merged error: 0.0b

Counts

113 → 15

regimes565.0ms

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	37	29
1	37	29

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4679×	body	1280	valid
1.4s	1888×	body	640	valid
268.0ms	551×	body	320	valid
114.0ms	672×	body	80	valid
64.0ms	210×	body	160	valid

Details

sample258.0ms

simplify9.0ms

prune5.0ms

localize32.0ms

rewrite23.0ms

series193.0ms

simplify107.0ms

prune326.0ms

localize37.0ms

rewrite24.0ms

series284.0ms

simplify45.0ms

prune408.0ms

localize38.0ms

rewrite33.0ms

series387.0ms

simplify61.0ms

prune462.0ms

localize40.0ms

rewrite33.0ms

series393.0ms

simplify61.0ms

prune386.0ms

regimes565.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.5s

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