Details

sample412.0ms

Algorithm

intervals

Results

223.0ms	115×	body	1280	valid
131.0ms	85×	body	640	valid
24.0ms	29×	body	320	valid
6.0ms	11×	body	160	valid
4.0ms	16×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.8b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b	(cos (- lambda1 lambda2))
2.4b	(sin (- lambda1 lambda2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

series236.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
153.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify1.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
4	2001
3	1179
2	486
1	211
0	101

prune569.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.8b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b	(cos (- lambda1 lambda2))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

82.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))

series430.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
24.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
160.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	2013
3	2013
2	917
1	312
0	128

prune805.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

95.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
15.0ms	(* (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))))))
18.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
89.0ms	(* (sin lambda1) (sin lambda2))
30.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
382.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	2010
3	2010
2	1330
1	380
0	148

prune909.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
10×	`add-log-exp`
8×	`associate-*r/`
6×	`associate-+r+`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 79

Calls

4 calls:

51.0ms	(cbrt (* (* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
8.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
13.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
9.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt (* (* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
306.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
330.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
358.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.6s

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
2	2003
1	465
0	152

prune922.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes937.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample14.1s

Algorithm

intervals

Results

8.4s	3607×	body	1280	valid
3.3s	2345×	body	640	valid
1.6s	937×	body	320	valid
225.0ms	419×	body	160	valid
225.0ms	692×	body	80	valid