Details

sample1.3s

Algorithm

intervals

Results

846.0ms	140×	body	1280	valid
105.0ms	68×	body	640	valid
99.0ms	31×	body	320	valid
10.0ms	9×	body	160	valid
4.0ms	1×	body	2560	valid
3.0ms	8×	body	80	valid

simplify142.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
3	34
2	33
1	26
0	17

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize163.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

69.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
38.0ms	(cos (- lambda1 lambda2))

series635.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
285.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
47.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
46.0ms	(cos (- lambda1 lambda2))

simplify7.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	2915
2	754
1	278
0	125

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize244.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 76

Calls

4 calls:

39.0ms	(* (sin phi1) (sin phi2))
31.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
169.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (sin phi1) (sin phi2))
437.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
555.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
109.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1897
1	516
0	187

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize220.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 68

Calls

4 calls:

27.0ms	(* (sin lambda1) (sin lambda2))
28.0ms	(* (sin phi1) (sin phi2))
28.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
8.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (sin lambda1) (sin lambda2))
106.0ms	(* (sin phi1) (sin phi2))
423.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
92.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

simplify8.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
4	2878
3	1437
2	618
1	278
0	138

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize344.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.5b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod` `cos-mult`
5×	`add-log-exp`
4×	`log-pow` `insert-posit16`
3×	`acos-asin` `frac-times` `log-prod` `associate-r` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
2×	`flip3-+` `exp-diff` `frac-add` `flip-+` `sin-mult`
1×	`distribute-rgt-in` `log-div` `distribute-lft-in` `rem-log-exp` `associate-l` `associate-l/` `-commutative` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

181.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
8.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
24.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

601.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
358.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
157.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
156.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1617
1	444
0	164

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

regimes4.2s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample18.4s

Algorithm

intervals

Results

13.0s	4773×	body	1280	valid
3.4s	2117×	body	640	valid
1.0s	666×	body	320	valid
201.0ms	18×	body	2560	valid
143.0ms	278×	body	160	valid
38.0ms	150×	body	80	valid