Details

sample294.0ms

Algorithm

intervals

Results

172.0ms	111×	body	1280	valid
67.0ms	79×	body	640	valid
23.0ms	34×	body	320	valid
5.0ms	20×	body	80	valid
4.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize63.0ms

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))))
3.5b	(sin (- lambda1 lambda2))
3.6b	(cos (- lambda1 lambda2))

rewrite48.0ms

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`
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 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(sin (- lambda1 lambda2))
15.0ms	(cos (- lambda1 lambda2))

series217.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
142.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(sin (- lambda1 lambda2))
32.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1502
2	528
1	207
0	97

prune569.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize97.0ms

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)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b	(cos (- lambda1 lambda2))

rewrite103.0ms

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`
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 → 54

Calls

4 calls:

59.0ms	(* (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)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
27.0ms	(cos (- lambda1 lambda2))

series374.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
136.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
2	1276
1	310
0	124

prune876.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `sin-mult`
2×	`+-commutative` `associate-*l/` `frac-add`
1×	`associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
36.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
14.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (sin lambda2))
313.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
39.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
209.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify1.7s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1612
1	342
0	133

prune726.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize182.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)) (* (cos lambda2) (* (cos lambda1) (cos phi2))))))
0.3b	(+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b	(* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))
1.9b	(- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

118×	`pow1`
66×	`pow-prod-down`
57×	`associate-*r/`
50×	`cos-mult`
42×	`add-cbrt-cube` `add-exp-log`
27×	`prod-exp` `cbrt-unprod`
19×	`frac-add`
13×	`add-sqr-sqrt` `frac-times` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`cube-unmult`
9×	`associate-*l/` `pow-sqr` `pow-prod-up` `associate-/l/`
8×	`add-log-exp`
7×	`associate-/r/`
5×	`sum-cubes`
4×	`associate-/l*`
3×	`associate-/r*` `flip3-+` `pow-plus` `flip3--` `flip-+` `flip--`
2×	`sqr-cos` `associate-+r+`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `swap-sqr` `div-exp` `associate-r` `associate-l` `*-commutative` `div-inv`

Counts

4 → 143

Calls

4 calls:

909.0ms	(/ (+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)) (* (cos lambda2) (* (cos lambda1) (cos phi2))))))
399.0ms	(+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
444.0ms	(* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))
26.0ms	(- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)) (* (cos lambda2) (* (cos lambda1) (cos phi2))))))
286.0ms	(+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
137.0ms	(* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))
205.0ms	(- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1))

simplify1.8s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
1	874
0	283

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	48
1	48
0	33

end0.0ms

sample10.9s

Algorithm

intervals

Results

6.1s	3488×	body	1280	valid
3.1s	2375×	body	640	valid
977.0ms	976×	body	320	valid
201.0ms	435×	body	160	valid
118.0ms	726×	body	80	valid