Details

sample501.0ms

Algorithm

intervals

Results

280.0ms	115×	body	1280	valid
165.0ms	85×	body	640	valid
20.0ms	21×	body	320	valid
7.0ms	26×	body	80	valid
6.0ms	9×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize45.0ms

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))))
2.4b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`cos-diff`
2×	`cos-sum` `associate-+r+` `sub-neg` `sin-sum` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `associate-l` `sin-diff` `flip-+`

Counts

4 → 46

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
38.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
168.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))
39.0ms	(sin (- lambda1 lambda2))

simplify2.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
4	2616
3	1179
2	486
1	211
0	101

prune440.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.4b	(cos (- lambda1 lambda2))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`associate-l` `insert-posit16`
3×	`cos-diff` `associate-r`
2×	`cos-sum` `associate-+r+` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

25.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
39.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos lambda1) (sin lambda2))
21.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
158.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms	(cos (- lambda1 lambda2))

simplify1.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5005
3	2585
2	726
1	276
0	122

prune670.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
4×	`associate-+r+` `insert-posit16`
3×	`+-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`sum-log` `flip3-+` `flip-+` `sin-mult`

Counts

4 → 65

Calls

4 calls:

13.0ms	(* (cos lambda1) (sin lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
449.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos lambda1) (sin lambda2))
88.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
291.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	4599
2	1021
1	338
0	140

prune753.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(exp (+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
0.7b	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`associate-+r+` `exp-sum`
11×	`add-sqr-sqrt`
10×	`exp-prod`
9×	`+-commutative` `log-prod` `add-cube-cbrt` `add-log-exp`
7×	`pow1` `add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `associate-l` `log-pow` `distribute-lft-out`
4×	`insert-posit16`
3×	`associate-r`
2×	`sum-log` `rem-log-exp` `rem-exp-log`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

23.0ms	(* (sin lambda1) (sin lambda2))
1.7s	(exp (+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))
493.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
1.8s	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin lambda1) (sin lambda2))
411.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))
330.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
728.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	3864
2	874
1	329
0	146

prune763.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes960.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	34
1	34
0	24

end0.0ms

sample16.1s

Algorithm

intervals

Results

9.3s	3541×	body	1280	valid
5.0s	2316×	body	640	valid
1.0s	985×	body	320	valid
280.0ms	416×	body	160	valid
198.0ms	742×	body	80	valid