Details

sample887.0ms

Algorithm

intervals

Results

487.0ms	140×	body	1280	valid
185.0ms	68×	body	640	valid
100.0ms	31×	body	320	valid
12.0ms	9×	body	160	valid
4.0ms	1×	body	2560	valid
3.0ms	8×	body	80	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
3	36
2	33
1	26
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize84.0ms

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))

rewrite72.0ms

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:

43.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

series269.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
55.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
36.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1282
1	278
0	125

prune568.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize61.0ms

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))))))

rewrite119.0ms

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:

15.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
88.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin phi1) (sin phi2))
119.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
306.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2888
1	518
0	187

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize138.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

46×	`associate-*r/`
28×	`cos-mult` `sin-mult`
24×	`frac-times`
22×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l/`
14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `flip3-+` `frac-add` `add-cube-cbrt` `flip-+`
9×	`flip3--` `frac-sub` `flip--` `sub-div`
8×	`pow1` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-l` `associate-*l/`
4×	`cbrt-undiv` `div-exp` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`acos-asin` `clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 119

Calls

4 calls:

10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
479.0ms	(/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
133.0ms	(* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
304.0ms	(/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
252.0ms	(* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
30.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.5s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
1	792
0	261

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.9b

localize107.0ms

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))))))

rewrite87.0ms

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:

75.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
58.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
25.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
30.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	2357
1	448
0	164

prune907.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.9b

regimes1.9s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample23.2s

Algorithm

intervals

Results

16.7s	4773×	body	1280	valid
4.9s	2117×	body	640	valid
866.0ms	666×	body	320	valid
200.0ms	278×	body	160	valid
146.0ms	18×	body	2560	valid
56.0ms	150×	body	80	valid