Details

sample940.0ms

Algorithm

intervals

Results

706.0ms	152×	body	1280	valid
84.0ms	63×	body	640	valid
27.0ms	24×	body	320	valid
5.0ms	9×	body	160	valid
2.0ms	8×	body	80	valid

simplify33.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize80.0ms

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)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b	(cos (- lambda1 lambda2))

rewrite47.0ms

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` `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 → 57

Calls

4 calls:

23.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
12.0ms	(cos (- lambda1 lambda2))

series305.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
90.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
55.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	2887
2	737
1	275
0	121

prune783.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite44.0ms

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×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
20.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sin phi1) (sin phi2))
65.0ms	(* (sin lambda1) (sin lambda2))
102.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
4	3001
3	1446
2	622
1	277
0	134

prune983.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))

rewrite59.0ms

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×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

16.0ms	(* (sin phi1) (sin phi2))
18.0ms	(* (sin lambda2) (sin lambda1))
20.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin phi1) (sin phi2))
58.0ms	(* (sin lambda2) (sin lambda1))
136.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))) R)
35.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))

simplify3.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
4	3086
3	1541
2	670
1	280
0	134

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.8b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))))) R)
0.3b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))))
0.8b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 58

Calls

4 calls:

12.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))))) R)
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))))
7.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))

series219.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))))) R)
64.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))))
24.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))))
30.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))))

simplify3.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
6	2878
5	1466
4	1027
3	760
2	409
1	190
0	103

prune756.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

regimes1.9s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample17.6s

Algorithm

intervals

Results

12.6s	4761×	body	1280	valid
3.8s	2133×	body	640	valid
604.0ms	685×	body	320	valid
133.0ms	281×	body	160	valid
33.0ms	134×	body	80	valid
27.0ms	7×	body	2560	valid